Research ArticleThe Effect of Shadow Banking on the Systemic Risk in a DynamicComplex Interbank Network System

Hong Fan and Hongjie Pan

Glorious Sun School of Business and Management Donghua University Shanghai 200051 China

Correspondence should be addressed to Hong Fan hongfandhueducn

Received 4 February 2020 Revised 4 April 2020 Accepted 15 April 2020 Published 18 May 2020

Guest Editor Baogui Xin

Copyright copy 2020 Hong Fan andHongjie Pan)is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

After the financial crisis triggered by the subprime mortgage crisis in the United States in 2008 many scholars believed that theunstable transmission of shadow banking business in the banking system is the main factor causing financial turmoil )is paperproposes a dynamic complex interbank network system model with shadow banking in which the dynamic complex interbanknetwork system differs from the traditional banking network and is formed by the interrelated business between shadow banksand commercial banks to explore the effect of shadow banking on the systemic risk )e results show that the existence of shadowbanking will increase the systemic risk accelerate the speed of bankruptcy of banks reduce the survival ratio of banks and increasethe strength of central bank assistance )e smaller the number of shadow banks in the system the higher the degree of creditconnection among commercial banks and the smaller the systemic risk

1 Introduction

)e outbreak of the global financial crisis has shown that theoccurrence of systemic risk would lead to a tremendousdestructive effect on the financial system [1 2] )ereforethe research of the systemic risk has drawn more and moreattention [3 4] In the existing studies of systemic risk mostof them focus on the analysis of the systemic risk that isconducted from the perspective of interbank lending and itis believed that interbank lending relationship has an im-portant impact on the systemic risk [5ndash7] )e networkstructure formed by interbank lending as a carrier of riskcontagion [8 9] plays an important role in the systemic risk[6 7] Kaufman and Scott [10] argued that the systemic riskwill be triggered by risks or possible systemic collapses in theinterbank lending market Allen and Gale [11] studied theeffects of a complete market structure and an incompletemarket structure on the systemic risk and found that thecomplete market structure is more stable than the incom-plete market structure Iori and Jafarey [12] found that thehomogeneous banking system is more stable than the het-erogeneous banking system Nier et al [13] pointed out that

the impact of banking network concentration on the sys-temic risk is nonmonotonous Lenzu and Tedeschi [14]analyzed the impact of different network topologies on thesystemic risk and found that the random network structureis more stable than the scale-free network structure Caccioliet al [15] showed that the scale-free network has betterflexibility but its systemic risk is significantly higher thanother networks Godlewski et al [16] argued that the small-world network structure is conducive to enhancing assetsconnectivity between banks reducing loan spreads and thesystemic risk Georg et al [17 18] stressed that the centralbank stabilizes interbank markets in the short run alone andthe money-centric network is more stable than the randomnetwork Lux [19] presented that the interbank networkshows a ldquocore peripheryrdquo structure )e core banks couldprovide financial support for peripheral banks to preventsystemic risk Berardi and Tedeschi [20] showed that thebanking network presents a centralized structure and theincrease in the number of attractive banks will reduce thesystemic risk

)e existing studies mainly analyzed the systemic riskcaused by the crisis from the perspective of the interbank

HindawiComplexityVolume 2020 Article ID 3951892 10 pageshttpsdoiorg10115520203951892

market and different interbank lending networks )e effectof shadow banking on systemic risk is almost lacking Asdefined in Page and Wooder [21] shadow banks are non-bank financial institutions that operate outside the tradi-tional banking regulation system Shadow banks are notdirectly regulated by central banks and they are not includedin the safety net According to Financial Stability Board(FSB) [22] the shadow banking system is a credit inter-mediary system which is free from the formal bankingsystem andmay cause systemic financial risks and regulatoryarbitrage risks )e FSB also sets out several classes ofshadow banking sectors (i) sectors susceptible to runs suchas certain mutual funds credit hedge funds and real-estatefunds (ii) nonbank lenders dependent on short-termfunding such as finance companies leasing companiesfactoring companies and consumer-credit companies (iii)market intermediaries dependent on short-term funding oron the secured funding of client assets such as brokerdealers (iv) companies facilitating credit creation such ascredit insurance companies financial guarantors andmonoline insurers and (v) securitization-based intermedi-aries Shadow banking brings prosperity to the financialmarket but at the same time it also brings great vulnera-bility to the financial system )erefore the interest in theimpact of shadow banking on financial markets is becominga growing area within systemic risk literature Pozsar et al[23] and Tucker [24] discussed that the size of shadowbanking showed a pattern of sudden increase before theoutbreak of the global financial crisis and shadow bankingwas considered as one of the main reasons that could triggerfinancial systemic risk Bernanke et al [25] believed thatshadow banking utilizes the balance sheets to provide creditloans similar to commercial banks and uses term conversionto avoid bankruptcy risk which induces systemic risk Di-amond [26] found that the diversification of shadowbankingrsquos portfolio by buying and selling risky loans wouldresult in the accumulation of the systemic risk Gennaioliet al [27] used an improved shadow banking model to studythe relationship between shadow banking and the systemicrisk and discovered if reasonably expected shadow bankingcould help withstand the systemic risk and maintain thesystem stable Elgin and Oztunali [28] found through a two-sector dynamic general equilibrium model that the relativesize of shadow banking sector will affect systemic riskColombo et al [29] constructed a shadow banking model toemphasize that the form of propagation after a crisis shockwill reduce the ability of the financial system to resist futureshocks and the level of the systemic risk will increase

Although the above research concerning the impact ofshadow banking on the systemic risk examines the rela-tionship between shadow banking and the systemic risk itdoes not reveal the mechanism of systemic risk well as theyneglected the complicated interactions among banks It iswidely believed that the systemic risk mainly originated fromthe cascading failures of banks due to the complicated in-teractions among banks )erefore the study of the impactof shadow banking on the systemic risk should be integratedwith the interbank network system In view of the aboveconsiderations a dynamic complex interbank network

system model with shadow banking is proposed )e dy-namic evolution of the systematic risk in the existence andabsence of shadow banking is studied in this study fur-thermore the impact of shadow banking on the number ofdefault banks bank survival rate ratio of default rate tocommercial bank survival rate and central bank assistanceare compared Moreover the time course of the systemic risk(dynamic evolutional systemic risk) other than a fixedsystemic risk is obtained in this paper as the calculation ofthe systemic risk is based on a dynamic interbank networkmodel )is enables us to observe the trend of the systemicrisk making the results of shadow banking effect on thesystemic risk more valuable

2 Model of a Dynamic Complex InterbankNetwork System with Shadow Banking

21eStructure of InterbankNetworkwith ShadowBankingA dynamic complex interbank network system with shadowbanking is constructed in which commercial banks andshadow banks form a network including connections to thereal economy here the real economy represents the rest ofeconomy namely the economy outside of banking )enumber of agents of commercial banks is denoted by M andN is the number of agents of shadow banks)usU M + N is the sum of all the banks in the systemWhen N 0 the interbank network system can be regardedas the traditional interbank network system t (t 1 2 middotmiddotmiddot) isthe dynamic evolution time step of the system At any time tthere are a finite number of banksU Figure 1 shows thestructure of interbank network with shadow bankingCommercial banks are overseen by the central bank )eyare operating within the protection net provided by thecentral bank and receive the central bankrsquos aid like CB

jt when

bank j defaults According to the definition proposed byPozsar et al [23] shadow banks are financial institutionsthat operate outside of the central bankrsquos regulatory )usthere is no need for shadow banks to obey the central bankrsquosregulations (such as legal reserves and investment restric-tions) Meanwhile they cannot receive aid from the centralbank

In the banking system bank failure is often caused by alack of liquidity )e liquidity of a bank is mainly related todeposit financing investment and interbank lendingWhen banks are short of liquidity they will borrow fromeach other in the interbank network which is shown inFigure 1 )e directed line segments between banks rep-resent the amounts of borrowing or lending from one bankto another For example the arrow from commercial bankMj points to commercial bank Mk indicating that com-mercial bank Mj is the debt bank of commercial bank Mkand its debt is b

jkt the arrow from commercial bank Mk

points to commercial bank Mi indicating that commercialbank Mi is commercial bank Mkrsquos creditor bank with a claimof bki

t Since shadow banks have the characteristics of in-dependence and information opacity [30] there is a businessrelationship between shadow banks and commercial bankswhile no interbank lending between shadow banks is con-sidered in this paper For example b

j|Mq|Nt indicates that

2 Complexity

commercial bank Mj borrows from shadow bank Nq andb

w|Nj|Mt indicates that shadow bank Nw borrows fromcommercial bank Mj b

q|Nk|Mt and b

k|Ml|Nt represent the

interbank claims and debts between commercial bank Mk

and shadow bank Nq and shadow bank Nl respectivelySimilarly bl|Ni|M

t and bi|Mw|Nt represent the interbank claims

and debts between commercial bank Mi and shadow bankNl and shadow bank Nw respectively Moreover accordingto the policy restrictions on the relationship betweencommercial banks and shadow banks in our model theinterbank lending relationship between a shadow bank andcommercial banks will be limited by the number (thenumber is represented by d that is the maximum number ofcommercial banks that a shadow bank can borrow)

In addition to interbank interactions in order to be morein line with the real financial state according to the researchof Gong and Page [31] the model proposed in this paperincludes connections to the real economy Sn To simplify thesystem this paper divides the state of the real economy intothree that is Sn(n= 123) )e banking system and realeconomy feature a two-sided interaction)e state of the realeconomy influences the banking system by determining theallocation of investment For each state of the real economythere is an investment project Kn(n= 1 2 3) As shown inFigure 1 a bank selects project Kn to invest in the realeconomy Sn )e return of the projects Kn is subject to thestate of the real economy (detailed in the below section)With reference to Paretorsquos principle [32] using Paretorsquoseconomic model [33] and taking the bank default rate (theratio of the number of default banks to the total number ofbanks) as a measure the three critical values for dividing thereal economy are calculated When the bank default rate isless than 10 it is in a good economic case S1 corre-sponding to the investment project K1 with low risk andhigh return when the bank default rate is between 10 and20 it is in a stable economic case S2 corresponding to theinvestment project K2 with medium risk and return whenthe bank default rate exceeds 20 it is in a depressedeconomic case S3 corresponding to the investment projectK3 with high risk and low return )e real economy Sn willchange with the dynamic evolution of the bank default ratein the system Banks in the system will default but thenumber of banks will not increase

22 Traditional Interbank Network System )e traditionalinterbank network refers to the network formed by theinterbank lending of commercial banks)is paper refers tothe studies of Iori et al [12] and Georg et al [17 18] andthe interbank network is set up as a random network In arandom network banks are randomly connected and theconnectivity relationship is represented by binary matrix JJij is either one or zero Jij 1 indicates that there is acredit linkage between bank i and bank j and Jij 0 meansthat there is no relationship c indicates the probability of acredit linkage between any two banks ie c isin[01] At oneextreme c 0 means there is no interbank lending whilec 1 means interbank networkrsquos structure is a fully con-nected structure

)e bank dynamic evolution is based on the banksrsquobalance sheet Every bankrsquos assets and liabilities in thebanking system are dynamically changing at each time step)e balance sheet of each bank in the system evolves dy-namically as follows

Litminus 1 A

itminus 1 + B

itminus 1 + V

itminus 1 minus 1113944

τ

j1I

itminus j (1)

where Litminus 1 is the liquidity asset of bank i at time t-1 Ai

tminus 1 isthe deposit of bank i at time t-1Vi

tminus 1 is the ownerrsquos equity ofbank i at time t-1 1113936

τj1 Ii

jminus s is the total investment of bank i

in τ investment periods and Bitminus 1 1113936

Uk1 bik

tminus 1 is the totalborrowing amount of bank i at time t-1 bik

tminus 1 gt 0 if bank i

borrows from bank k and bkitminus 1lt0 if bank k loans to bank i

where biktminus 1 minus bki

tminus 1 biktminus 1 minus bki

tminus 1 0 if there is no lendingrelationship between banks

23 Interbank Network System with Shadow BankingBesides the dynamically changing assets and liabilities ofevery bank the interbank lending network also changesdynamically at each time step It should be noted that there isno interbank lending between shadow banks in this paper)erefore the binary matrix J among shadow banks is al-ways set to zero )e balance sheet of banks in the interbanknetwork system with shadow banking is evolved same asequation (1) however if bank i is a shadow bank then Bi

tminus 1

1113936dk1 bi|N k|M

tminus 1 indicating the total borrowing amount ofshadow bank i at time t minus 1 bi|N k|M

tminus 1 gt 0 if shadow bank i

borrows from commercial bank k and bi|Nk|Mtminus 1 lt 0 if com-

mercial bank k borrows from to shadow bank i wherebi|N k|M

tminus 1 minus bi|N k|Mtminus 1 bi|N k|M

tminus 1 = minus bi|Nk|Mtminus 1 = 0 if there is no

lending relationship between shadow bank i and commercialbank k )e sequence of activities in each time is as followsAt the start of each time each bank inherits the initial li-quidity asset )en the liquidity asset of banks will changedynamically with the inflow and outflow of funds )e li-quidity asset of bank i is updated to

Lit L

itminus 1 + A

it minus A

itminus 11113872 1113873 minus raA

itminus 1 + ρ1113944

τ

j1I

itminus j + I

itminus τ (2)

where raAitminus 1 is the interest paid by the commercial bank to

depositors or the interest paid by the shadow bank to fi-nanciers and ra is the deposit interest rate or the financinginterest rate ρ1113936

τj1 Ii

tminus j and Iitminus τ are investment income and

the investment recovered at maturity and ρ is the rate ofreturn on investment of each time Since the deposit andfinancing patterns of customers are fluctuating and un-predictable each bank receives stochastic shocks to its li-quidity reserves )erefore it is assumed that the deposits orfinancing Ai

t for the bank i obeys the normal distributionAi

t = |A + AδAεt| εtsimN(01) where A is the mean of randomdeposits of commercial banks or random financing ofshadow banks and δA is the standard deviation of com-mercial banksrsquo random deposits or shadow banksrsquo randomfinancing

If Lit gt 0 it denotes that bank i has sufficient liquidity

Such bank can undertake dividend payments to

Complexity 3

shareholders Dividend distribution is different in com-mercial banks and shadow banks When bank i is a com-mercial bank dividend distribution Di|M

t can be described asfollows

Di|Mt max 0 min ρ1113944

τ

j1I

itminus j minus raA

itminus 1 L

it minus R

it L

it

⎡⎢⎢⎣⎡⎢⎢⎣

+ 1113944τminus 1

j1I

itminus j minus (1 + χ)A

it⎤⎦⎤⎦

(3)

where Rit βAi

t is the legal deposit reserve kept by com-mercial bank i β is the deposit reserve ratio and χ is thedeposit ratio When bank i is a shadow bank dividenddistribution Di|N

t is as follows

Di|Nt max 0 min χ ρ1113944

τ

j1I

itminus j minus raA

itminus 1

⎛⎝ ⎞⎠ Lit

⎡⎢⎢⎣ ⎤⎥⎥⎦⎡⎢⎢⎣ ⎤⎥⎥⎦ (4)

where χ is the financing ratio for simplicity the financingratio is equal to the deposit ratio in this paper

After the dividends have been paid the bank undertakesreinvestment Corresponding to the real economy Sn bank i

chooses project Kn to reinvest under its available liquidityand investment opportunity Different projects have dif-ferent returns on investment As the value of n increases theeconomic condition declines and the return on investmentdecreases )e return on investment of the project can beexpressed as

Ro | Sn

0 1 minus pn

Rsn

o pn

1113896 (n 1 2 3) (5)

where Rsn

o is the investment return corresponding to projectKn under the state of the real economy Sn )e value of Rsn

o is

set according to the existing investment return rate of banksand the loan income rate of finanical companies pn is theinvestment recovery probability corresponding to projectKn indicating the risk of the project with the increase of therisk of the project the investment recovery probabilitydecreases And the initial value is set by referring to the realbankrsquos nonperforming loan interest ratio )e better the realeconomy the lower the risk and the higher the return ofinvestment and the investment recovery probability

)e reinvestment of commercial bank i is Ii|Mt |Kn and

the reinvestment of shadow bank i is Ii|Nt |Kn

Ii|Mt | K

n min max 0 L

it minus D

i|Mt minus R

it1113960 1113961ωi

t1113960 1113961 (6)

Ii|Nt | K

n min max 0 L

it minus D

i|Nt1113960 1113961ωi

t1113960 1113961 (7)

where ωit is the investment opportunity of bank i )e in-

vestment opportunity of bank i at time t is subject to anormal distribution ωi

t |ω + ωδωηt| ηt sim N(01) ω is theaverage investment opportunity of banks and δω is thestandard deviation of banksrsquo investment opportunity )edifference between the two types of reinvestment is thatthere is no need for shadow banks to pay the legal depositreserve to the central bank

After completing the above dividend distribution andreinvestment if bank irsquos liquidity asset Li

t ge 0 it can continueinterbank lending Conversely if Li

t lt 0 bank i becomes amember of defaulted set F at time step t When defaultedbank i is a commercial bank even if it is unable to borrowenough money to restore its liquidity it can go back to thebanking system because it will be bailed out by the centralbank )e form of the assistance of the central bank will bedescribed as follows

Traditional commercial banks interbanklending network

Commercialbank Mj

Commercialbank Mi

Commercialbank Mk

Centralbank

Shadowbank Nw

Shadowbank Nl

Shadowbank Nq

Realeconomy

Realeconomy

Realeconomy

Sn

Sn

Sn

Kn Kn

Sn

Sn

Kn

Kn

Kn

Sn

Kn

bti|Mw|N

bt1|Ni|M

btk|Ml|Nbt

q|Nk|M

btw|Nj|M

btj|Mq|N bt

kibtjk

CBti

CBtk

CBtj

Figure 1 )e structure of interbank network with shadow banking

4 Complexity

CBit

Rit minus Li

t Rit gtLi

t

0 otherwise1113896 (8)

When Rit gt Li

t the central bankrsquos assistance amount tocommercial bank i is Ri

t minus Lit After getting the assistance of

the central bank commercial bank irsquos debts update to 0(Bi

t 0) and go into the next time step Otherwise thecommercial bank i pays legal deposit reserve by itself andevolves to the next time step Protected by the central bankcommercial banks only default and do not go bankrupt

Alternatively if a bank experiencing negative liquidity isa shadow bank i (ie Li

tlt0) it will be cleared by the centralbank Following Eisenberg and Noe [34] this paper assumesthat shadow banks with insufficient liquidity to cover theirdebts pay their debts proportionally )e debt repayment iscalculated as follows

PBi|Nk|Mt

Vi|Nt lowast

bi|Nk|Mt

1113936dk1b

i|Nk|Mt

if bi|Nk|Mt gt0

and Vi|Nt gt0

0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

where Vi|Nt represents the ownerrsquos equity of shadow bank i

bi|Nk|Mt is the loan amount of commercial bank k to shadow

bank i and 1113936dk1 b

i|N k|Mt is the total amount of shadow bank i

borrowed from no more than d commercial banks d is thenumber of commercial banks that is borrowed by shadowbank i )en the shadow bank irsquos debts update to 0 and itbecomes a member of bankrupt setD

24 Dynamic Process Algorithm of Interbank Network SystemwithShadowBanking In the interbank network system withshadow banking banks conduct interbank lending whentheir liquidity is insufficient including interbank lendingamong commercial banks and business relationship betweencommercial banks and shadow banks )e dynamic processalgorithm of the interbank network with shadow banking isshown in Figure 2 which is divided into the following 4steps

Step 1 at time t 1 the initial real economy Snis set toS1 and the initial calculation of the initial deposit of thecommercial banks the initial financing of the shadowbank and each parameter and variable is respectivelyperformedStep 2 the real economy Sn is determined and the assetliquidity Lt of each bank at time t is calculatedAccording to the number of default banks at time t-1the bank default rate is calculated to determine the realeconomy Sn in time t and the value of relevant pa-rameters is determined by Sn )en the liquidity of thesurvival bank at time t is calculated the banks withsufficient liquidity (Lt gt 0) carry out dividend distri-bution Dt and reinvestment It and the banks that lack

liquidity (Lt le 0) enter into Step 3 and start interbanklendingStep 3 according to the liquidity of each bank in Step 2the bank with liquidity Lt gt 0 is the creditor bank andthe bank with liquidity Lt le 0 is the debt bank )e debtbank and the creditor bank establish a connectionthrough a random network and conduct interbanklending according to the liquidity of the banks If thedebt bank j can borrow sufficient funds from thecreditor banks to repay the previous loan and interestie L

jt minus (1 + rb)B

jtminus 1 ge 0 (rb is the interbank lending

rate) bank j enters the next time step if the debt bank j

cannot borrow sufficient funds to repay the previousloan and interest ie L

jt minus (1 + rb)B

jtminus 1 lt 0 the debt

bank j becomes a member of defaulted set F and getsinto Step 4Step 4 the insolvent default debt bank is bailed out orcleared If the default bank j is a shadow bank it willpartially repay the debt according to its ownerrsquos equityand then get into the bankruptcy set D if the defaultbank j is a commercial bank the central bank will aid itto make its liquidity meet the legal deposit reserve )edebts of banks which are bailed out or cleared updateto 0 (Bj

t 0)

3 Simulation and Analysis

)e interbank network system with shadow banking con-structed in this paper can simulate the real dynamic evo-lutionary process of the interbank network system )ebankrsquos balance sheet is dynamically evolved such as liquidityL ownerrsquos equity V deposit A and investment I Relatedindicators will change dynamically over time t By observingthe dynamic evolution process of the interbank networksystem the impact of shadow banking on the systemic risk isstudied Due to the heterogeneity of banks banks in theinterbank network will be exposed to risks owing to differentoperating conditions and business strategies resulting in aseries of and even large-scale chain failure )e systemicrisk of the interbank network is not only affected by thebanksrsquo own factors (internal factors) but also by shadowbanking (external factors) To objectively reflect the effect ofshadow banking on the banking system and measure thesystemic risk of the banking network the average number ofdefault banks in the [t+1 t+T] time zone was normalizedand the calculated value was recorded as Risk(t) It is cal-culated as follows

Risk(t) 1

TRe

1113944

Re

i11113944

t+T

jt+1

Cij

Sij

(10)

where the T is the time interval and the average proportionof default banks in the future T time (that is the averageprobability of default banks) can indicate the systemic risk ofthe system at a certain moment )is paper sets T 10 Re isthe time number of the simulation Ci

j is the number ofbanks that default at time j in the ith simulation and Si

j is thenumber of banks that survived at time j in the ith simulation

Complexity 5

400 banks were selected as research objects (sufficient toreflect the characteristics of the banking network system)including 100 commercial banks (M100) and 300 shadowbanks (N300) and the maximum simulation time step wasset to t 100 (the simulated 100-step system has approachedstability)

31 e Impact of Shadow Banking on the Systemic RiskFigure 3 plots the systemic risk of the interbank networkwith the existence of shadow banking and no shadowbanking over time It can be seen from Figure 3 that in anycase the systemic risk exists from the beginning of thesimulation which is related to the heterogeneity of thebanks Different banks have different operating activities

which lead to the initial risk of the banking system It isfurther found that although there is a systemic risk in thebanking system with no shadow banking its value fluctuatesonly within a small range close to 0 and is relatively stableHowever the systemic risk of the system with shadowbanking has been relatively high and fluctuating whichindicates that shadow banking is affected by the high-riskcharacteristics of its own business activities which will bringsignificant systemic risk impact to the banking system Withthe extension of time steps the systemic risk has shown adownward trend )is may be due to the bankruptcy of theshadow bank which caused the termination of the interbanklending between the shadow bank and the commercial bankAt the same time the banking system can self-regulatedigestive risks which is also an important reason to resist

t = 1 time beginningS = S1

Determine the real economy Sn andcalculate the liquidity Lt of each bank

at the beginning of period t

Adequate liquidityLt gt 0

Debtbank

Creditor bank

Dividenddistribution Dt

and investment It

Interbank lending

Interbank lendingcompleted

Take bank j from the debtbank set

Ltj ndash (1 + rb)Bt

j ge 0

Put bank j into defaultingset F

Bank j is a commercialbank

Bank j is cleared its debtupdates to 0 (Bt

j = 0) and itgoes to bankruptcy set D

Central bank assistscommercial bank j and itsdebts update to 0 (Bt

j = 0)

All debt banks havebeen processed

t = t + 1

t gt 100

End

Randomly selectinganother debt bank

No Yes

No

Yes

No

Yes

YesNo

No

Yes

No

Yes

Figure 2 Dynamic process algorithm of the interbank system with shadow banking

6 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

commercial bank Mj borrows from shadow bank Nq andb

w|Nj|Mt indicates that shadow bank Nw borrows fromcommercial bank Mj b

q|Nk|Mt and b

k|Ml|Nt represent the

interbank claims and debts between commercial bank Mk

and shadow bank Nq and shadow bank Nl respectivelySimilarly bl|Ni|M

t and bi|Mw|Nt represent the interbank claims

and debts between commercial bank Mi and shadow bankNl and shadow bank Nw respectively Moreover accordingto the policy restrictions on the relationship betweencommercial banks and shadow banks in our model theinterbank lending relationship between a shadow bank andcommercial banks will be limited by the number (thenumber is represented by d that is the maximum number ofcommercial banks that a shadow bank can borrow)

In addition to interbank interactions in order to be morein line with the real financial state according to the researchof Gong and Page [31] the model proposed in this paperincludes connections to the real economy Sn To simplify thesystem this paper divides the state of the real economy intothree that is Sn(n= 123) )e banking system and realeconomy feature a two-sided interaction)e state of the realeconomy influences the banking system by determining theallocation of investment For each state of the real economythere is an investment project Kn(n= 1 2 3) As shown inFigure 1 a bank selects project Kn to invest in the realeconomy Sn )e return of the projects Kn is subject to thestate of the real economy (detailed in the below section)With reference to Paretorsquos principle [32] using Paretorsquoseconomic model [33] and taking the bank default rate (theratio of the number of default banks to the total number ofbanks) as a measure the three critical values for dividing thereal economy are calculated When the bank default rate isless than 10 it is in a good economic case S1 corre-sponding to the investment project K1 with low risk andhigh return when the bank default rate is between 10 and20 it is in a stable economic case S2 corresponding to theinvestment project K2 with medium risk and return whenthe bank default rate exceeds 20 it is in a depressedeconomic case S3 corresponding to the investment projectK3 with high risk and low return )e real economy Sn willchange with the dynamic evolution of the bank default ratein the system Banks in the system will default but thenumber of banks will not increase

22 Traditional Interbank Network System )e traditionalinterbank network refers to the network formed by theinterbank lending of commercial banks)is paper refers tothe studies of Iori et al [12] and Georg et al [17 18] andthe interbank network is set up as a random network In arandom network banks are randomly connected and theconnectivity relationship is represented by binary matrix JJij is either one or zero Jij 1 indicates that there is acredit linkage between bank i and bank j and Jij 0 meansthat there is no relationship c indicates the probability of acredit linkage between any two banks ie c isin[01] At oneextreme c 0 means there is no interbank lending whilec 1 means interbank networkrsquos structure is a fully con-nected structure

)e bank dynamic evolution is based on the banksrsquobalance sheet Every bankrsquos assets and liabilities in thebanking system are dynamically changing at each time step)e balance sheet of each bank in the system evolves dy-namically as follows

Litminus 1 A

itminus 1 + B

itminus 1 + V

itminus 1 minus 1113944

τ

j1I

itminus j (1)

where Litminus 1 is the liquidity asset of bank i at time t-1 Ai

tminus 1 isthe deposit of bank i at time t-1Vi

tminus 1 is the ownerrsquos equity ofbank i at time t-1 1113936

τj1 Ii

jminus s is the total investment of bank i

in τ investment periods and Bitminus 1 1113936

Uk1 bik

tminus 1 is the totalborrowing amount of bank i at time t-1 bik

tminus 1 gt 0 if bank i

borrows from bank k and bkitminus 1lt0 if bank k loans to bank i

where biktminus 1 minus bki

tminus 1 biktminus 1 minus bki

tminus 1 0 if there is no lendingrelationship between banks

23 Interbank Network System with Shadow BankingBesides the dynamically changing assets and liabilities ofevery bank the interbank lending network also changesdynamically at each time step It should be noted that there isno interbank lending between shadow banks in this paper)erefore the binary matrix J among shadow banks is al-ways set to zero )e balance sheet of banks in the interbanknetwork system with shadow banking is evolved same asequation (1) however if bank i is a shadow bank then Bi

tminus 1

1113936dk1 bi|N k|M

tminus 1 indicating the total borrowing amount ofshadow bank i at time t minus 1 bi|N k|M

tminus 1 gt 0 if shadow bank i

borrows from commercial bank k and bi|Nk|Mtminus 1 lt 0 if com-

mercial bank k borrows from to shadow bank i wherebi|N k|M

tminus 1 minus bi|N k|Mtminus 1 bi|N k|M

tminus 1 = minus bi|Nk|Mtminus 1 = 0 if there is no

lending relationship between shadow bank i and commercialbank k )e sequence of activities in each time is as followsAt the start of each time each bank inherits the initial li-quidity asset )en the liquidity asset of banks will changedynamically with the inflow and outflow of funds )e li-quidity asset of bank i is updated to

Lit L

itminus 1 + A

it minus A

itminus 11113872 1113873 minus raA

itminus 1 + ρ1113944

τ

j1I

itminus j + I

itminus τ (2)

where raAitminus 1 is the interest paid by the commercial bank to

depositors or the interest paid by the shadow bank to fi-nanciers and ra is the deposit interest rate or the financinginterest rate ρ1113936

τj1 Ii

tminus j and Iitminus τ are investment income and

the investment recovered at maturity and ρ is the rate ofreturn on investment of each time Since the deposit andfinancing patterns of customers are fluctuating and un-predictable each bank receives stochastic shocks to its li-quidity reserves )erefore it is assumed that the deposits orfinancing Ai

t for the bank i obeys the normal distributionAi

t = |A + AδAεt| εtsimN(01) where A is the mean of randomdeposits of commercial banks or random financing ofshadow banks and δA is the standard deviation of com-mercial banksrsquo random deposits or shadow banksrsquo randomfinancing

If Lit gt 0 it denotes that bank i has sufficient liquidity

Such bank can undertake dividend payments to

Complexity 3

shareholders Dividend distribution is different in com-mercial banks and shadow banks When bank i is a com-mercial bank dividend distribution Di|M

t can be described asfollows

Di|Mt max 0 min ρ1113944

τ

j1I

itminus j minus raA

itminus 1 L

it minus R

it L

it

⎡⎢⎢⎣⎡⎢⎢⎣

+ 1113944τminus 1

j1I

itminus j minus (1 + χ)A

it⎤⎦⎤⎦

(3)

where Rit βAi

t is the legal deposit reserve kept by com-mercial bank i β is the deposit reserve ratio and χ is thedeposit ratio When bank i is a shadow bank dividenddistribution Di|N

t is as follows

Di|Nt max 0 min χ ρ1113944

τ

j1I

itminus j minus raA

itminus 1

⎛⎝ ⎞⎠ Lit

⎡⎢⎢⎣ ⎤⎥⎥⎦⎡⎢⎢⎣ ⎤⎥⎥⎦ (4)

where χ is the financing ratio for simplicity the financingratio is equal to the deposit ratio in this paper

After the dividends have been paid the bank undertakesreinvestment Corresponding to the real economy Sn bank i

chooses project Kn to reinvest under its available liquidityand investment opportunity Different projects have dif-ferent returns on investment As the value of n increases theeconomic condition declines and the return on investmentdecreases )e return on investment of the project can beexpressed as

Ro | Sn

0 1 minus pn

Rsn

o pn

1113896 (n 1 2 3) (5)

where Rsn

o is the investment return corresponding to projectKn under the state of the real economy Sn )e value of Rsn

o is

set according to the existing investment return rate of banksand the loan income rate of finanical companies pn is theinvestment recovery probability corresponding to projectKn indicating the risk of the project with the increase of therisk of the project the investment recovery probabilitydecreases And the initial value is set by referring to the realbankrsquos nonperforming loan interest ratio )e better the realeconomy the lower the risk and the higher the return ofinvestment and the investment recovery probability

)e reinvestment of commercial bank i is Ii|Mt |Kn and

the reinvestment of shadow bank i is Ii|Nt |Kn

Ii|Mt | K

n min max 0 L

it minus D

i|Mt minus R

it1113960 1113961ωi

t1113960 1113961 (6)

Ii|Nt | K

n min max 0 L

it minus D

i|Nt1113960 1113961ωi

t1113960 1113961 (7)

where ωit is the investment opportunity of bank i )e in-

vestment opportunity of bank i at time t is subject to anormal distribution ωi

t |ω + ωδωηt| ηt sim N(01) ω is theaverage investment opportunity of banks and δω is thestandard deviation of banksrsquo investment opportunity )edifference between the two types of reinvestment is thatthere is no need for shadow banks to pay the legal depositreserve to the central bank

After completing the above dividend distribution andreinvestment if bank irsquos liquidity asset Li

t ge 0 it can continueinterbank lending Conversely if Li

t lt 0 bank i becomes amember of defaulted set F at time step t When defaultedbank i is a commercial bank even if it is unable to borrowenough money to restore its liquidity it can go back to thebanking system because it will be bailed out by the centralbank )e form of the assistance of the central bank will bedescribed as follows

Traditional commercial banks interbanklending network

Commercialbank Mj

Commercialbank Mi

Commercialbank Mk

Centralbank

Shadowbank Nw

Shadowbank Nl

Shadowbank Nq

Realeconomy

Realeconomy

Realeconomy

Sn

Sn

Sn

Kn Kn

Sn

Sn

Kn

Kn

Kn

Sn

Kn

bti|Mw|N

bt1|Ni|M

btk|Ml|Nbt

q|Nk|M

btw|Nj|M

btj|Mq|N bt

kibtjk

CBti

CBtk

CBtj

Figure 1 )e structure of interbank network with shadow banking

4 Complexity

CBit

Rit minus Li

t Rit gtLi

t

0 otherwise1113896 (8)

When Rit gt Li

t the central bankrsquos assistance amount tocommercial bank i is Ri

t minus Lit After getting the assistance of

the central bank commercial bank irsquos debts update to 0(Bi

t 0) and go into the next time step Otherwise thecommercial bank i pays legal deposit reserve by itself andevolves to the next time step Protected by the central bankcommercial banks only default and do not go bankrupt

Alternatively if a bank experiencing negative liquidity isa shadow bank i (ie Li

tlt0) it will be cleared by the centralbank Following Eisenberg and Noe [34] this paper assumesthat shadow banks with insufficient liquidity to cover theirdebts pay their debts proportionally )e debt repayment iscalculated as follows

PBi|Nk|Mt

Vi|Nt lowast

bi|Nk|Mt

1113936dk1b

i|Nk|Mt

if bi|Nk|Mt gt0

and Vi|Nt gt0

0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

where Vi|Nt represents the ownerrsquos equity of shadow bank i

bi|Nk|Mt is the loan amount of commercial bank k to shadow

bank i and 1113936dk1 b

i|N k|Mt is the total amount of shadow bank i

borrowed from no more than d commercial banks d is thenumber of commercial banks that is borrowed by shadowbank i )en the shadow bank irsquos debts update to 0 and itbecomes a member of bankrupt setD

24 Dynamic Process Algorithm of Interbank Network SystemwithShadowBanking In the interbank network system withshadow banking banks conduct interbank lending whentheir liquidity is insufficient including interbank lendingamong commercial banks and business relationship betweencommercial banks and shadow banks )e dynamic processalgorithm of the interbank network with shadow banking isshown in Figure 2 which is divided into the following 4steps

Step 1 at time t 1 the initial real economy Snis set toS1 and the initial calculation of the initial deposit of thecommercial banks the initial financing of the shadowbank and each parameter and variable is respectivelyperformedStep 2 the real economy Sn is determined and the assetliquidity Lt of each bank at time t is calculatedAccording to the number of default banks at time t-1the bank default rate is calculated to determine the realeconomy Sn in time t and the value of relevant pa-rameters is determined by Sn )en the liquidity of thesurvival bank at time t is calculated the banks withsufficient liquidity (Lt gt 0) carry out dividend distri-bution Dt and reinvestment It and the banks that lack

liquidity (Lt le 0) enter into Step 3 and start interbanklendingStep 3 according to the liquidity of each bank in Step 2the bank with liquidity Lt gt 0 is the creditor bank andthe bank with liquidity Lt le 0 is the debt bank )e debtbank and the creditor bank establish a connectionthrough a random network and conduct interbanklending according to the liquidity of the banks If thedebt bank j can borrow sufficient funds from thecreditor banks to repay the previous loan and interestie L

jt minus (1 + rb)B

jtminus 1 ge 0 (rb is the interbank lending

rate) bank j enters the next time step if the debt bank j

cannot borrow sufficient funds to repay the previousloan and interest ie L

jt minus (1 + rb)B

jtminus 1 lt 0 the debt

bank j becomes a member of defaulted set F and getsinto Step 4Step 4 the insolvent default debt bank is bailed out orcleared If the default bank j is a shadow bank it willpartially repay the debt according to its ownerrsquos equityand then get into the bankruptcy set D if the defaultbank j is a commercial bank the central bank will aid itto make its liquidity meet the legal deposit reserve )edebts of banks which are bailed out or cleared updateto 0 (Bj

t 0)

3 Simulation and Analysis

)e interbank network system with shadow banking con-structed in this paper can simulate the real dynamic evo-lutionary process of the interbank network system )ebankrsquos balance sheet is dynamically evolved such as liquidityL ownerrsquos equity V deposit A and investment I Relatedindicators will change dynamically over time t By observingthe dynamic evolution process of the interbank networksystem the impact of shadow banking on the systemic risk isstudied Due to the heterogeneity of banks banks in theinterbank network will be exposed to risks owing to differentoperating conditions and business strategies resulting in aseries of and even large-scale chain failure )e systemicrisk of the interbank network is not only affected by thebanksrsquo own factors (internal factors) but also by shadowbanking (external factors) To objectively reflect the effect ofshadow banking on the banking system and measure thesystemic risk of the banking network the average number ofdefault banks in the [t+1 t+T] time zone was normalizedand the calculated value was recorded as Risk(t) It is cal-culated as follows

Risk(t) 1

TRe

1113944

Re

i11113944

t+T

jt+1

Cij

Sij

(10)

where the T is the time interval and the average proportionof default banks in the future T time (that is the averageprobability of default banks) can indicate the systemic risk ofthe system at a certain moment )is paper sets T 10 Re isthe time number of the simulation Ci

j is the number ofbanks that default at time j in the ith simulation and Si

j is thenumber of banks that survived at time j in the ith simulation

Complexity 5

400 banks were selected as research objects (sufficient toreflect the characteristics of the banking network system)including 100 commercial banks (M100) and 300 shadowbanks (N300) and the maximum simulation time step wasset to t 100 (the simulated 100-step system has approachedstability)

31 e Impact of Shadow Banking on the Systemic RiskFigure 3 plots the systemic risk of the interbank networkwith the existence of shadow banking and no shadowbanking over time It can be seen from Figure 3 that in anycase the systemic risk exists from the beginning of thesimulation which is related to the heterogeneity of thebanks Different banks have different operating activities

which lead to the initial risk of the banking system It isfurther found that although there is a systemic risk in thebanking system with no shadow banking its value fluctuatesonly within a small range close to 0 and is relatively stableHowever the systemic risk of the system with shadowbanking has been relatively high and fluctuating whichindicates that shadow banking is affected by the high-riskcharacteristics of its own business activities which will bringsignificant systemic risk impact to the banking system Withthe extension of time steps the systemic risk has shown adownward trend )is may be due to the bankruptcy of theshadow bank which caused the termination of the interbanklending between the shadow bank and the commercial bankAt the same time the banking system can self-regulatedigestive risks which is also an important reason to resist

t = 1 time beginningS = S1

Determine the real economy Sn andcalculate the liquidity Lt of each bank

at the beginning of period t

Adequate liquidityLt gt 0

Debtbank

Creditor bank

Dividenddistribution Dt

and investment It

Interbank lending

Interbank lendingcompleted

Take bank j from the debtbank set

Ltj ndash (1 + rb)Bt

j ge 0

Put bank j into defaultingset F

Bank j is a commercialbank

Bank j is cleared its debtupdates to 0 (Bt

j = 0) and itgoes to bankruptcy set D

Central bank assistscommercial bank j and itsdebts update to 0 (Bt

j = 0)

All debt banks havebeen processed

t = t + 1

t gt 100

End

Randomly selectinganother debt bank

No Yes

No

Yes

No

Yes

YesNo

No

Yes

No

Yes

Figure 2 Dynamic process algorithm of the interbank system with shadow banking

6 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

shareholders Dividend distribution is different in com-mercial banks and shadow banks When bank i is a com-mercial bank dividend distribution Di|M

t can be described asfollows

Di|Mt max 0 min ρ1113944

τ

j1I

itminus j minus raA

itminus 1 L

it minus R

it L

it

⎡⎢⎢⎣⎡⎢⎢⎣

+ 1113944τminus 1

j1I

itminus j minus (1 + χ)A

it⎤⎦⎤⎦

(3)

where Rit βAi

t is the legal deposit reserve kept by com-mercial bank i β is the deposit reserve ratio and χ is thedeposit ratio When bank i is a shadow bank dividenddistribution Di|N

t is as follows

Di|Nt max 0 min χ ρ1113944

τ

j1I

itminus j minus raA

itminus 1

⎛⎝ ⎞⎠ Lit

⎡⎢⎢⎣ ⎤⎥⎥⎦⎡⎢⎢⎣ ⎤⎥⎥⎦ (4)

where χ is the financing ratio for simplicity the financingratio is equal to the deposit ratio in this paper

After the dividends have been paid the bank undertakesreinvestment Corresponding to the real economy Sn bank i

chooses project Kn to reinvest under its available liquidityand investment opportunity Different projects have dif-ferent returns on investment As the value of n increases theeconomic condition declines and the return on investmentdecreases )e return on investment of the project can beexpressed as

Ro | Sn

0 1 minus pn

Rsn

o pn

1113896 (n 1 2 3) (5)

where Rsn

o is the investment return corresponding to projectKn under the state of the real economy Sn )e value of Rsn

o is

set according to the existing investment return rate of banksand the loan income rate of finanical companies pn is theinvestment recovery probability corresponding to projectKn indicating the risk of the project with the increase of therisk of the project the investment recovery probabilitydecreases And the initial value is set by referring to the realbankrsquos nonperforming loan interest ratio )e better the realeconomy the lower the risk and the higher the return ofinvestment and the investment recovery probability

)e reinvestment of commercial bank i is Ii|Mt |Kn and

the reinvestment of shadow bank i is Ii|Nt |Kn

Ii|Mt | K

n min max 0 L

it minus D

i|Mt minus R

it1113960 1113961ωi

t1113960 1113961 (6)

Ii|Nt | K

n min max 0 L

it minus D

i|Nt1113960 1113961ωi

t1113960 1113961 (7)

where ωit is the investment opportunity of bank i )e in-

vestment opportunity of bank i at time t is subject to anormal distribution ωi

t |ω + ωδωηt| ηt sim N(01) ω is theaverage investment opportunity of banks and δω is thestandard deviation of banksrsquo investment opportunity )edifference between the two types of reinvestment is thatthere is no need for shadow banks to pay the legal depositreserve to the central bank

After completing the above dividend distribution andreinvestment if bank irsquos liquidity asset Li

t ge 0 it can continueinterbank lending Conversely if Li

t lt 0 bank i becomes amember of defaulted set F at time step t When defaultedbank i is a commercial bank even if it is unable to borrowenough money to restore its liquidity it can go back to thebanking system because it will be bailed out by the centralbank )e form of the assistance of the central bank will bedescribed as follows

Traditional commercial banks interbanklending network

Commercialbank Mj

Commercialbank Mi

Commercialbank Mk

Centralbank

Shadowbank Nw

Shadowbank Nl

Shadowbank Nq

Realeconomy

Realeconomy

Realeconomy

Sn

Sn

Sn

Kn Kn

Sn

Sn

Kn

Kn

Kn

Sn

Kn

bti|Mw|N

bt1|Ni|M

btk|Ml|Nbt

q|Nk|M

btw|Nj|M

btj|Mq|N bt

kibtjk

CBti

CBtk

CBtj

Figure 1 )e structure of interbank network with shadow banking

4 Complexity

CBit

Rit minus Li

t Rit gtLi

t

0 otherwise1113896 (8)

When Rit gt Li

t the central bankrsquos assistance amount tocommercial bank i is Ri

t minus Lit After getting the assistance of

the central bank commercial bank irsquos debts update to 0(Bi

t 0) and go into the next time step Otherwise thecommercial bank i pays legal deposit reserve by itself andevolves to the next time step Protected by the central bankcommercial banks only default and do not go bankrupt

Alternatively if a bank experiencing negative liquidity isa shadow bank i (ie Li

tlt0) it will be cleared by the centralbank Following Eisenberg and Noe [34] this paper assumesthat shadow banks with insufficient liquidity to cover theirdebts pay their debts proportionally )e debt repayment iscalculated as follows

PBi|Nk|Mt

Vi|Nt lowast

bi|Nk|Mt

1113936dk1b

i|Nk|Mt

if bi|Nk|Mt gt0

and Vi|Nt gt0

0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

where Vi|Nt represents the ownerrsquos equity of shadow bank i

bi|Nk|Mt is the loan amount of commercial bank k to shadow

bank i and 1113936dk1 b

i|N k|Mt is the total amount of shadow bank i

borrowed from no more than d commercial banks d is thenumber of commercial banks that is borrowed by shadowbank i )en the shadow bank irsquos debts update to 0 and itbecomes a member of bankrupt setD

24 Dynamic Process Algorithm of Interbank Network SystemwithShadowBanking In the interbank network system withshadow banking banks conduct interbank lending whentheir liquidity is insufficient including interbank lendingamong commercial banks and business relationship betweencommercial banks and shadow banks )e dynamic processalgorithm of the interbank network with shadow banking isshown in Figure 2 which is divided into the following 4steps

Step 1 at time t 1 the initial real economy Snis set toS1 and the initial calculation of the initial deposit of thecommercial banks the initial financing of the shadowbank and each parameter and variable is respectivelyperformedStep 2 the real economy Sn is determined and the assetliquidity Lt of each bank at time t is calculatedAccording to the number of default banks at time t-1the bank default rate is calculated to determine the realeconomy Sn in time t and the value of relevant pa-rameters is determined by Sn )en the liquidity of thesurvival bank at time t is calculated the banks withsufficient liquidity (Lt gt 0) carry out dividend distri-bution Dt and reinvestment It and the banks that lack

liquidity (Lt le 0) enter into Step 3 and start interbanklendingStep 3 according to the liquidity of each bank in Step 2the bank with liquidity Lt gt 0 is the creditor bank andthe bank with liquidity Lt le 0 is the debt bank )e debtbank and the creditor bank establish a connectionthrough a random network and conduct interbanklending according to the liquidity of the banks If thedebt bank j can borrow sufficient funds from thecreditor banks to repay the previous loan and interestie L

jt minus (1 + rb)B

jtminus 1 ge 0 (rb is the interbank lending

rate) bank j enters the next time step if the debt bank j

cannot borrow sufficient funds to repay the previousloan and interest ie L

jt minus (1 + rb)B

jtminus 1 lt 0 the debt

bank j becomes a member of defaulted set F and getsinto Step 4Step 4 the insolvent default debt bank is bailed out orcleared If the default bank j is a shadow bank it willpartially repay the debt according to its ownerrsquos equityand then get into the bankruptcy set D if the defaultbank j is a commercial bank the central bank will aid itto make its liquidity meet the legal deposit reserve )edebts of banks which are bailed out or cleared updateto 0 (Bj

t 0)

3 Simulation and Analysis

)e interbank network system with shadow banking con-structed in this paper can simulate the real dynamic evo-lutionary process of the interbank network system )ebankrsquos balance sheet is dynamically evolved such as liquidityL ownerrsquos equity V deposit A and investment I Relatedindicators will change dynamically over time t By observingthe dynamic evolution process of the interbank networksystem the impact of shadow banking on the systemic risk isstudied Due to the heterogeneity of banks banks in theinterbank network will be exposed to risks owing to differentoperating conditions and business strategies resulting in aseries of and even large-scale chain failure )e systemicrisk of the interbank network is not only affected by thebanksrsquo own factors (internal factors) but also by shadowbanking (external factors) To objectively reflect the effect ofshadow banking on the banking system and measure thesystemic risk of the banking network the average number ofdefault banks in the [t+1 t+T] time zone was normalizedand the calculated value was recorded as Risk(t) It is cal-culated as follows

Risk(t) 1

TRe

1113944

Re

i11113944

t+T

jt+1

Cij

Sij

(10)

where the T is the time interval and the average proportionof default banks in the future T time (that is the averageprobability of default banks) can indicate the systemic risk ofthe system at a certain moment )is paper sets T 10 Re isthe time number of the simulation Ci

j is the number ofbanks that default at time j in the ith simulation and Si

j is thenumber of banks that survived at time j in the ith simulation

Complexity 5

400 banks were selected as research objects (sufficient toreflect the characteristics of the banking network system)including 100 commercial banks (M100) and 300 shadowbanks (N300) and the maximum simulation time step wasset to t 100 (the simulated 100-step system has approachedstability)

31 e Impact of Shadow Banking on the Systemic RiskFigure 3 plots the systemic risk of the interbank networkwith the existence of shadow banking and no shadowbanking over time It can be seen from Figure 3 that in anycase the systemic risk exists from the beginning of thesimulation which is related to the heterogeneity of thebanks Different banks have different operating activities

which lead to the initial risk of the banking system It isfurther found that although there is a systemic risk in thebanking system with no shadow banking its value fluctuatesonly within a small range close to 0 and is relatively stableHowever the systemic risk of the system with shadowbanking has been relatively high and fluctuating whichindicates that shadow banking is affected by the high-riskcharacteristics of its own business activities which will bringsignificant systemic risk impact to the banking system Withthe extension of time steps the systemic risk has shown adownward trend )is may be due to the bankruptcy of theshadow bank which caused the termination of the interbanklending between the shadow bank and the commercial bankAt the same time the banking system can self-regulatedigestive risks which is also an important reason to resist

t = 1 time beginningS = S1

Determine the real economy Sn andcalculate the liquidity Lt of each bank

at the beginning of period t

Adequate liquidityLt gt 0

Debtbank

Creditor bank

Dividenddistribution Dt

and investment It

Interbank lending

Interbank lendingcompleted

Take bank j from the debtbank set

Ltj ndash (1 + rb)Bt

j ge 0

Put bank j into defaultingset F

Bank j is a commercialbank

Bank j is cleared its debtupdates to 0 (Bt

j = 0) and itgoes to bankruptcy set D

Central bank assistscommercial bank j and itsdebts update to 0 (Bt

j = 0)

All debt banks havebeen processed

t = t + 1

t gt 100

End

Randomly selectinganother debt bank

No Yes

No

Yes

No

Yes

YesNo

No

Yes

No

Yes

Figure 2 Dynamic process algorithm of the interbank system with shadow banking

6 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

CBit

Rit minus Li

t Rit gtLi

t

0 otherwise1113896 (8)

When Rit gt Li

t the central bankrsquos assistance amount tocommercial bank i is Ri

t minus Lit After getting the assistance of

the central bank commercial bank irsquos debts update to 0(Bi

t 0) and go into the next time step Otherwise thecommercial bank i pays legal deposit reserve by itself andevolves to the next time step Protected by the central bankcommercial banks only default and do not go bankrupt

Alternatively if a bank experiencing negative liquidity isa shadow bank i (ie Li

tlt0) it will be cleared by the centralbank Following Eisenberg and Noe [34] this paper assumesthat shadow banks with insufficient liquidity to cover theirdebts pay their debts proportionally )e debt repayment iscalculated as follows

PBi|Nk|Mt

Vi|Nt lowast

bi|Nk|Mt

1113936dk1b

i|Nk|Mt

if bi|Nk|Mt gt0

and Vi|Nt gt0

0 otherwise

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

where Vi|Nt represents the ownerrsquos equity of shadow bank i

bi|Nk|Mt is the loan amount of commercial bank k to shadow

bank i and 1113936dk1 b

i|N k|Mt is the total amount of shadow bank i

borrowed from no more than d commercial banks d is thenumber of commercial banks that is borrowed by shadowbank i )en the shadow bank irsquos debts update to 0 and itbecomes a member of bankrupt setD

24 Dynamic Process Algorithm of Interbank Network SystemwithShadowBanking In the interbank network system withshadow banking banks conduct interbank lending whentheir liquidity is insufficient including interbank lendingamong commercial banks and business relationship betweencommercial banks and shadow banks )e dynamic processalgorithm of the interbank network with shadow banking isshown in Figure 2 which is divided into the following 4steps

Step 1 at time t 1 the initial real economy Snis set toS1 and the initial calculation of the initial deposit of thecommercial banks the initial financing of the shadowbank and each parameter and variable is respectivelyperformedStep 2 the real economy Sn is determined and the assetliquidity Lt of each bank at time t is calculatedAccording to the number of default banks at time t-1the bank default rate is calculated to determine the realeconomy Sn in time t and the value of relevant pa-rameters is determined by Sn )en the liquidity of thesurvival bank at time t is calculated the banks withsufficient liquidity (Lt gt 0) carry out dividend distri-bution Dt and reinvestment It and the banks that lack

liquidity (Lt le 0) enter into Step 3 and start interbanklendingStep 3 according to the liquidity of each bank in Step 2the bank with liquidity Lt gt 0 is the creditor bank andthe bank with liquidity Lt le 0 is the debt bank )e debtbank and the creditor bank establish a connectionthrough a random network and conduct interbanklending according to the liquidity of the banks If thedebt bank j can borrow sufficient funds from thecreditor banks to repay the previous loan and interestie L

jt minus (1 + rb)B

jtminus 1 ge 0 (rb is the interbank lending

rate) bank j enters the next time step if the debt bank j

cannot borrow sufficient funds to repay the previousloan and interest ie L

jt minus (1 + rb)B

jtminus 1 lt 0 the debt

bank j becomes a member of defaulted set F and getsinto Step 4Step 4 the insolvent default debt bank is bailed out orcleared If the default bank j is a shadow bank it willpartially repay the debt according to its ownerrsquos equityand then get into the bankruptcy set D if the defaultbank j is a commercial bank the central bank will aid itto make its liquidity meet the legal deposit reserve )edebts of banks which are bailed out or cleared updateto 0 (Bj

t 0)

3 Simulation and Analysis

)e interbank network system with shadow banking con-structed in this paper can simulate the real dynamic evo-lutionary process of the interbank network system )ebankrsquos balance sheet is dynamically evolved such as liquidityL ownerrsquos equity V deposit A and investment I Relatedindicators will change dynamically over time t By observingthe dynamic evolution process of the interbank networksystem the impact of shadow banking on the systemic risk isstudied Due to the heterogeneity of banks banks in theinterbank network will be exposed to risks owing to differentoperating conditions and business strategies resulting in aseries of and even large-scale chain failure )e systemicrisk of the interbank network is not only affected by thebanksrsquo own factors (internal factors) but also by shadowbanking (external factors) To objectively reflect the effect ofshadow banking on the banking system and measure thesystemic risk of the banking network the average number ofdefault banks in the [t+1 t+T] time zone was normalizedand the calculated value was recorded as Risk(t) It is cal-culated as follows

Risk(t) 1

TRe

1113944

Re

i11113944

t+T

jt+1

Cij

Sij

(10)

where the T is the time interval and the average proportionof default banks in the future T time (that is the averageprobability of default banks) can indicate the systemic risk ofthe system at a certain moment )is paper sets T 10 Re isthe time number of the simulation Ci

j is the number ofbanks that default at time j in the ith simulation and Si

j is thenumber of banks that survived at time j in the ith simulation

Complexity 5

400 banks were selected as research objects (sufficient toreflect the characteristics of the banking network system)including 100 commercial banks (M100) and 300 shadowbanks (N300) and the maximum simulation time step wasset to t 100 (the simulated 100-step system has approachedstability)

31 e Impact of Shadow Banking on the Systemic RiskFigure 3 plots the systemic risk of the interbank networkwith the existence of shadow banking and no shadowbanking over time It can be seen from Figure 3 that in anycase the systemic risk exists from the beginning of thesimulation which is related to the heterogeneity of thebanks Different banks have different operating activities

which lead to the initial risk of the banking system It isfurther found that although there is a systemic risk in thebanking system with no shadow banking its value fluctuatesonly within a small range close to 0 and is relatively stableHowever the systemic risk of the system with shadowbanking has been relatively high and fluctuating whichindicates that shadow banking is affected by the high-riskcharacteristics of its own business activities which will bringsignificant systemic risk impact to the banking system Withthe extension of time steps the systemic risk has shown adownward trend )is may be due to the bankruptcy of theshadow bank which caused the termination of the interbanklending between the shadow bank and the commercial bankAt the same time the banking system can self-regulatedigestive risks which is also an important reason to resist

t = 1 time beginningS = S1

Determine the real economy Sn andcalculate the liquidity Lt of each bank

at the beginning of period t

Adequate liquidityLt gt 0

Debtbank

Creditor bank

Dividenddistribution Dt

and investment It

Interbank lending

Interbank lendingcompleted

Take bank j from the debtbank set

Ltj ndash (1 + rb)Bt

j ge 0

Put bank j into defaultingset F

Bank j is a commercialbank

Bank j is cleared its debtupdates to 0 (Bt

j = 0) and itgoes to bankruptcy set D

Central bank assistscommercial bank j and itsdebts update to 0 (Bt

j = 0)

All debt banks havebeen processed

t = t + 1

t gt 100

End

Randomly selectinganother debt bank

No Yes

No

Yes

No

Yes

YesNo

No

Yes

No

Yes

Figure 2 Dynamic process algorithm of the interbank system with shadow banking

6 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

400 banks were selected as research objects (sufficient toreflect the characteristics of the banking network system)including 100 commercial banks (M100) and 300 shadowbanks (N300) and the maximum simulation time step wasset to t 100 (the simulated 100-step system has approachedstability)

31 e Impact of Shadow Banking on the Systemic RiskFigure 3 plots the systemic risk of the interbank networkwith the existence of shadow banking and no shadowbanking over time It can be seen from Figure 3 that in anycase the systemic risk exists from the beginning of thesimulation which is related to the heterogeneity of thebanks Different banks have different operating activities

which lead to the initial risk of the banking system It isfurther found that although there is a systemic risk in thebanking system with no shadow banking its value fluctuatesonly within a small range close to 0 and is relatively stableHowever the systemic risk of the system with shadowbanking has been relatively high and fluctuating whichindicates that shadow banking is affected by the high-riskcharacteristics of its own business activities which will bringsignificant systemic risk impact to the banking system Withthe extension of time steps the systemic risk has shown adownward trend )is may be due to the bankruptcy of theshadow bank which caused the termination of the interbanklending between the shadow bank and the commercial bankAt the same time the banking system can self-regulatedigestive risks which is also an important reason to resist

t = 1 time beginningS = S1

Determine the real economy Sn andcalculate the liquidity Lt of each bank

at the beginning of period t

Adequate liquidityLt gt 0

Debtbank

Creditor bank

Dividenddistribution Dt

and investment It

Interbank lending

Interbank lendingcompleted

Take bank j from the debtbank set

Ltj ndash (1 + rb)Bt

j ge 0

Put bank j into defaultingset F

Bank j is a commercialbank

Bank j is cleared its debtupdates to 0 (Bt

j = 0) and itgoes to bankruptcy set D

Central bank assistscommercial bank j and itsdebts update to 0 (Bt

j = 0)

All debt banks havebeen processed

t = t + 1

t gt 100

End

Randomly selectinganother debt bank

No Yes

No

Yes

No

Yes

YesNo

No

Yes

No

Yes

Figure 2 Dynamic process algorithm of the interbank system with shadow banking

6 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

external shock and maintain the stability of the bankingsystem

32eImpactof ShadowBankingon theCumulativeNumberof Default Banks Bank Survival Rate Ratio of Bank DefaultRate to Commercial Bank Survival Rate and the Amount ofCentral Bank Assistance in the Banking System To effec-tively describe the specific performance of the impact ofthe existence of shadow banking on the systemic risk ofbanks we calculated the cumulative number of defaultbanks bank survival rate ratio of bank default rate tocommercial bank survival rate and the amount of centralbank assistance in the banking system through simulationFigure 4(a) shows the impact of the existence of shadowbanking on the cumulative number of default banks in thesystem It can be found that the cumulative number ofdefault banks in the banking system with shadow bankingis significantly higher than that of the banking system withno shadow banking and the difference between the two ismultiplied as the time step is extended When the time stepreaches 100 the cumulative number of default banks in thebanking system with no shadow banking is stable at 6while that in the banking system with shadow banking is ashigh as 20 )e existence of shadow banking can signifi-cantly increase the number of default banks within thesystem )e emergence of default banks under the exis-tence of shadow banking is mainly due to the decline inliquidity of the system caused by the interbank lendingbetween shadow banks and commercial banks Table 1shows the liquidity of the system under the existence ofshadow banking and no shadow banking at evolutionarytime Under the influence of business activities such as

investment the existence of shadow banking aggravatesthe interbank lending between shadow banks and com-mercial banks resulting in a significant decline in theliquidity of the system Debt banks cannot repay theirdebts on time resulting in an increase in the number ofdefault banks

Figure 4(b) shows the impact of the existence of shadowbanking on changes in bank survival ratio in the system Itcan be seen that the bank survival ratio in the bankingsystem with no shadow banking decreased with the ex-tension of the time step but the decline was relatively smalland the fluctuation was stable and finally stayed at around092 )is shows that the banking system with no shadowbanking is generally stable However the bank survival ratioin the banking system with shadow banking has shown anotable decline from the beginning As the time step isextended the rate of decline has not slowed down and thereis still a significant downward trend until 100 steps It showsthat the existence of shadow banking significantly reducesthe number of surviving banks in the system underminesthe stability of the banking system has a big shock on thebanking system and increases the possibility of inducingsystemic risk in the banking system )e condition ofcommercial banks in the banking system can directly reflectthe stability of the banking system and it is meaningful tocalculate the ratio of the bank default rate to the survival rateof commercial banks Figure 4(c) depicts the impact of theexistence of shadow banking on the ratio of bank default rateto commercial bank survival rate With the introduction ofshadow banking the contagion risk induced by shadowbanking results in the decline of commercial bank survivalratio and the increase of bank default rate the ratio of defaultrate to commercial bank survival rate is significantly higherthan that in the case with no shadow banking and ulti-mately the stability of the banking system is damagedFigure 4(d) shows the impact of the existence of shadowbanking on the change in the amount of central bank as-sistance )e central bank assistance to commercial bankscan be clearly observed from about 60 steps as shown in thefigure )e existence of shadow banking has significantlyaggravated the central bank assistance to commercial banks)is once again emphasizes the interbank lending betweenshadow banks and commercial banks will greatly reduce theliquidity of the system (as shown in Table 1))e bankruptcyof the shadow banks will cause commercial banks to fall intoa liquidity dilemma because they cannot recover the loanfunds on time Eventually commercial banks closed down)e ability of the system to withstand risks is reducedcausing systemic risk

33 e Impact of Changes in Correlation Indicators betweenShadow Banks and Commercial Banks on Systemic Risk ofBanks In the case of a finite number of banks in the systemthat isU 400 the combination of the number of shadowbanks and commercial banks will affect the scope of thelending between them and the liquidity of the system willchange and thus affect the systemic risk Figure 5 shows thesystemic risk curve under the number combination of three

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

Existence of shadow bankingNo shadow banking

Syste

mic

risk

Figure 3 )e impact of the existence of shadow banking on thesystemic risk (the parameters are set as followsra 00035 rb 0023 β 015 χ 03 σA 03 σω 003 c 003A 1000 ω I 500 ρ 0045 τ 3d 3 Rs1

o 007 Rs2

o 003Rs3

o 001 p1 095 p2 05 p3 03U 400 M 400 and N 0for the case of no shadow banking andM 100 and N 300 for thecase of existence of shadow banking)

Complexity 7

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

types of shadow banks and commercial banks (M N100 300 M N 200 200 andM N 300 100) It can be seenthat as the number of shadow banks in the system decreasesfrom 300 to 100 and the number of commercial banks in-creases from 100 to 300 the systemic risk gradually decreasesand tends to be stable and the possibility of bank default inthe system is also reduced It shows that the more thenumber of shadow banks in the banking system compared to

the number of commercial banks the greater the risk impactof the system)e high number of shadow banks will reducethe maintenance role of the regulatory authorities and thecentral bank on the stability of the banking system bring alarge and uncertain risk impact to the banking systemweaken the ability of the banking system to deal with risksand accelerate bank failure

Iori et al [12] and Georg [18] studied traditional bankingnetwork systems and pointed out that the higher the creditconnection between banks the lower the systemic risk Tofurther examine the impact of shadow banking on thesystemic risk Figure 6 plots the systemic risk changes underdifferent credit connections (c001 c 003 and c 005)between shadow banks and commercial banks )e result issimilar to the traditional view Under the structure of theinterbank network with shadow banking the higher thecredit connection between shadow banks and commercialbanks the lower and more stable the systemic risk )is

0 20 40 60 80 100Time step

0

5

10

15

20

No shadow bankingExistence of shadow banking

Cum

ulat

ive n

umbe

r of

defa

ult b

anks

(a)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

08

085

09

095

1

Bank

surv

ival

ratio

(b)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

0005

001

0015

002

0025

003

Bank

def

ault

rate

co

mm

erci

al b

ank

surv

ival

ratio

(c)

0 20 40 60 80 100Time step

No shadow bankingExistence of shadow banking

0

05

1

15

2

25

3

The a

mou

nt o

f cen

tral

ba

nk as

sista

nce

times104

(d)

Figure 4 (a) )e impact of the existence of shadow banking on the cumulative number of default banks in the banking system (b) )eimpact of the existence of shadow banking on changes in bank survival ratio in the banking system (c))e impact of the existence of shadowbanking on the ratio of bank default rate to commercial bank survival rate (d))e impact of the existence of shadow banking on the changesin the amount of central bank assistance (the parameter settings are the same as in Figure 3)

Table 1 )e liquidity of the system under the existence of shadowbanking and no shadow banking at evolutionary time

Time step20 40 60 80

Existence of shadowbanking 703193 746510 731807 729434

No shadow banking 739944 723973 751858 810823

8 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

illustrates that with the increase of the credit connectionbetween shadow banks and commercial banks the possi-bility of interbank lending between shadow banking andcommercial banks is increased )e existence of shadowbanking shares part of the systemic risk improves thestability of the banking system and reduces the possibility ofbankruptcy

4 Conclusions

)e growth of shadow banking has led to fundamentalchanges in the global financial architecture As an important

part of the contemporary complex financial system shadowbanking is considered to be one of the important reasons forcausing systemic risk In order to better explain the effect ofshadow banking on systemic risk a dynamic complex in-terbank network model with shadow banking is constructedin this paper Based on the traditional banking networkmodel the model used the relationship between shadowbanks and commercial banks to form a banking systemnetwork and analyzed the impact of shadow banking on thesystemic risk In addition the banksrsquo balance sheet and theinterbank lending network are dynamically evolved in thismodel which is closer to real bank operations and depictsthe specific impact of shadow banking on systemic risk froma microlevel )rough numerical simulation we have ob-tained a series of conclusions as follows

(i) Compared with the traditional banking networksystem the existence of shadow banking does affectthe systemic risk

(ii) )e existence of shadow banking will have an im-pact on the stability of the banking system resultingin an increase in the number of default banks in thesystem a decline in bank survival rates and anincrease in the number of central bank assistance)e liquidity of funds within the system is reducedwhich increases the occurrence of systemic risk

(iii) When the number of shadow banks is greater thanthe number of commercial banks the systemic riskwill be enormous However higher credit connec-tion between shadow banks and commercial bankswill reduce the systemic risk

)e aforementioned conclusions not only have prac-tical significance for quantitative research on the systemicrisk but also have important reference value for preventingfinancial risks In addition the definition of shadowbanking is different and the banking system is relativelycomplex )erefore there are still many problems that canbe discussed in future work for example governmentpolicy interference factors under macroeconomic condi-tions should be considered [35] a more in-depth networkstructure of interbank lending [36](not only random net-work) should be constructed and the real-world interbanklending network should be estimated by using real data

Data Availability

)e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is study was supported by the National Natural ScienceFoundation of China (71971054) the Shanghai NaturalScience Foundation (19ZR1402100) and the FundamentalResearch Funds for the Central Universities (19D110803)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

c = 001c = 003c = 005

Syste

mic

risk

Figure 6 )e impact of changes in credit connection betweenshadow banks and commercial banks on systemic risk curves (theparameter setting is the same as in Figure 3 except M 100N 300and c)

0 15 30 45 60 75 90Time step

0

0005

001

0015

002

0025

003

0035

MN = 100300MN = 200200MN = 300100

Syste

mic

risk

Figure 5 )e impact of the change in the number combinationbetween the shadow banks and the commercial banks on thesystemic risk curve (the parameter setting is the same as in Figure 3except for M and N)

Complexity 9

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity

References

[1] Y Jin and Z Zeng ldquoBanking risk and macroeconomicfluctuationsrdquo Journal of Banking amp Finance vol 48pp 350ndash360 2014

[2] S Poledna J L Molina-Borboa S Martınez-JaramilloM van der Leij and S )urner ldquo)e multi-layer networknature of systemic risk and its implications for the costs offinancial crisesrdquo Journal of Financial Stability vol 20pp 70ndash81 2015

[3] A R Neveu ldquoA survey of network-based analysis and sys-temic risk measurementrdquo Journal of Economic Interaction andCoordination vol 1 pp 1ndash41 2016

[4] M Pollak and Y Guan ldquoPartially overlapping ownership andcontagion in financial networksrdquo Complexity vol 2017 Ar-ticle ID 9895632 16 pages 2017

[5] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[6] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[7] T Schuler and L Corrado ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2016

[8] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[9] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[10] G G Kaufman and K E Scott ldquoWhat is systemic risk and dobank regulators retard or contribute to itrdquo Independent Re-view vol 7 no 3 pp 371ndash391 2003

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[13] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007

[14] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[15] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[16] C J Godlewski B Sanditov and T Burger-Helmchen ldquoBanklending networks experience reputation and borrowingcosts empirical evidence from the French syndicated lendingmarketrdquo Journal of Business Finance and Accounting vol 39no 1-2 pp 113ndash140 2012

[17] C P Georg and J Poschmann Systemic Risk in a NetworkModel of Interbank Markets with Central Bank Activity JenaEconomic Research Papers 2010

[18] C-P Georg ldquo)e effect of the interbank network structureon contagion and common shocksrdquo Journal of Banking ampFinance vol 37 no 7 pp 2216ndash2228 2013

[19] T Lux ldquoEmergence of a core-periphery structure in a simpledynamic model of the interbank marketrdquo Journal of EconomicDynamics and Control vol 52 pp A11ndashA23 2015

[20] S Berardi and G Tedeschi ldquoFrom banksrsquo strategies to fi-nancial (in)stabilityrdquo International Review of Economics ampFinance vol 47 pp 255ndash272 2017

[21] J H F Page and M Wooders ldquoNetworks and Stabilityrdquo inComputational Complexity R Meyers Ed pp 6024ndash6048Springer New York NY USA 2012

[22] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[23] Z Pozsar T Adrian A Ashcraft et al Shadow BankingFederal Reserve Bank of New York Staff Reports vol 105no 458 pp 447ndash457 New York NY USA 2010

[24] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 Oxford University PressLondon UK January 2010

[25] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[26] D W Diamond ldquoFinancial intermediation and delegatedmonitoringrdquo e Review of Economic Studies vol 51 no 3pp 393ndash414 1984

[27] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[28] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 no 2012 pp 1ndash482012

[29] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 no 9 pp 180ndash190 2016

[30] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[31] R Gong and F H Page ldquoShadow banks and systemic risksrdquoSSRN Electronic Journal 2015

[32] J M Juran ldquoPareto lorenz Bernoulli juran and othersrdquoIndustrial Quality Control vol 25 no 10 1960

[33] F Basile ldquoGreat management ideas can work for yourdquoIndianapolis Business Journal vol 16 no 1 pp 53-54 1996

[34] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[35] A R Admati P M DeMarzoM F Hellwig and P Pfleidererldquo)e leverage ratchet effectrdquo e Journal of Finance vol 73no 1 pp 145ndash198 2018

[36] S Gabrieli ldquo)e microstructure of the money market beforeand after the financial crisis a network perspectiverdquo SSRNElectronic Journal vol 9 no 181 2011

10 Complexity