Interbank network analysis - COMESA Monetary Institute …cmi.comesa.int/.../uploads/2014/06/Interbank-network-analysis.pdf · Interbank network analysis . 2 Key Question: If one

Interbank network analysis

2

Key Question:

If one bank were to face an adverse shock, how

would the rest of the banking / financial system be

affected?

Potential Solution:

Analysis using network modelling tools

Outline

Introduction

Why network models?

Approaches to network analysis

Constructing a network graph

3

Introduction

ULTIMATE GOAL: A model to examine the role of

financial contagion in the banking system, which also

seeks to obtain the aggregate losses for the financial

system.

Using network theory, we study the structure of the

banking system which is composed of banks that

are connected by their interbank bilateral

exposures.

4

Introduction

Where are network models used?

Intelligence agencies identify criminal and terrorist

networks from traces of communication that they

collect; and then identify key players in these networks.

Social networking websites like Facebook identify and

recommend potential friends based on friends-of-

friends.

Epidemiologists track spread of diseases.

Central banks for mapping interlinkages between FIs.

5

Introduction

Among central banks, who is using them?

Bank of England , Deutsche Bundesbank, European Central Bank,

Reserve Bank of India, South African Reserve Bank etc.

Most central banks favour network analysis because

Visual understanding

Uncover patterns in relationships or interactions which may not be readily

clear in the numbers.

Follow the paths that information (liquidity, panic) follows in financial

systems.

Once data is mapped as a network, it is easy to simulate the

propagation of systemic shocks and crises due to contagion.

6

Why network models?

Interconnectedness within the banking system proved to

be a key driver of systemic risk in the 2008 global financial

crisis.

The crisis emphasised how network linkages and

interactions between banks are critical to understanding

systemic risk.

It is important for financial stability analysts to have a

sound understanding of the level of and changes in

financial interconnectedness.

7

Why network models?

Viewing the banking system as a network is useful in analysing the

effects that the failure of a bank may produce.

It is important to understand how the risk of systemic breakdown

relates to the type and number of institutions that comprise the

banking system.

Furthermore, a study of the concentration of the banking system helps

us to focus on:

the role of direct interbank connections as a source of systemic risk,

the potential for knock-on defaults that are created by such exposures,

how adequately capital regulation would address the risk of systemic

breakdown that arises in the banking sector.

8

Why network models?

9

simultaneous failure of

banks

direct bilateral exposures between

banks

correlated exposures of

banks to a common source

of risk

informational contagion

feedback effects from endogenous

fire-sale of assets by distressed

institutions

Causes of simultaneous bank failure, Nier (2008)


Allen and Gale (2000)

Examine the different types of networks by completeness and

interconnected.

The connections created within interbank system can guard against

liquidity shocks, although these same interlinkages may act as

catalyst for multiple bank failures in the event of default by a single

institution.

In addition to investigating the response of different network

structures to the risk of contagion, they conclude that complete

claims structures are shown to be more robust than incomplete

structures.

10


11

Complete market

structure

Incomplete market

structure

Disconnected

incomplete market

structure

Types of networks, Allen and Gale (2000)


Sachs (2010)

Makes assumptions such as maximum entropy regarding the

structure of interbank exposures .

Finds that the stability of a financial system depends not only on

the completeness and interconnectedness of the network, but also

on the distribution of interbank exposures within the network.

A network with money centres with asset concentration among

core banks is likely to be more unstable than systems with banks of

homogeneous size in a random network.

A money centre is a network system where few large banks are strongly

interconnected and a large number of small banks in the periphery are

only connected to one core bank but not to other banks in the network.

12


13

A money centre model with 3 core banks, Sachs (2008)

Approaches to network analysis Minou and Reyes (2012):

Analyse the global banking network for 184 countries during 1978-2010.

Density of the global banking network defined by cross-border banking flows is pro-cyclical,

expanding and contracting with the global cycle of capital flows.

Connectedness in the network tends to rise before banking and debt crises and fall in the

aftermath.

Iori et al (2008), Nier et al (2008) and Li et al (2010) apply the theory of complex

networks in describing the interbank market.

Bank of Uganda:

Define the credit lending relationships of banks in the Ugandan interbank market using network

theory, enabling the study of various degrees of connectivity in the network over time in a

systematic way.

Examine how small changes in the underlying parameters can have a significant impact on the

stability of networks.

14


Type of data for interbank network analysis varies;

Direct interbank market bilateral exposures

For different types of markets and transactions e.g. secured and

unsecured lending, FX exposures, swaps, securities

Data from payments systems

Vary by size of transactions

Analysis can be performed for varied frequencies e.g. daily,

weekly or monthly.

Data is arranged in an adjacency matrix to reflect bilateral

exposures.

15


Each bank is represented by a node on the network,

and the bilateral interbank exposures of each bank

define the links with other banks.

These links may be directed or undirected

Directed network: interbank connections comprise both

assets and liabilities; no netting of exposures is

assumed.

Undirected network

Also, network may be weighted or unweighted.

16


17

A I B F J C E K D L M N G H A 0 1 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B 0 0 0 1 1 0 0 0 0 0 0 0 0 0 F 1 0 0 0 0 0 0 0 0 0 0 1 0 0 J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0 0 0 0 1 1 0 0 0 0 0 0 E 0 0 0 0 0 0 0 0 0 0 0 1 0 0 K 0 0 0 0 0 0 0 0 0 0 0 0 0 0 D 0 0 0 1 0 0 1 1 0 1 1 0 0 0 L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 0 0 0 0 0 0 0 0 0 0 0 0 0 0 N 1 0 0 1 1 0 1 1 0 0 1 0 0 0 G 0 0 0 0 0 0 0 0 0 0 0 1 0 0 H 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Unweighted networks


18

Unweighted networks


19

A I B F J C E K D L M N G H

A 0 1 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0

B 0 0 0 2.7 6.5 0 0 0 0 0 0 0 0 0

F 17.6 0 0 0 0 0 0 0 0 0 0 48.4 0 0

J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0 0 0 0 8.4 20 0 0 0 0 0 0 E 0 0 0 0 0 0 0 0 0 0 0 40 0 0

K 0 0 0 0 0 0 0 0 0 0 0 0 0 0 D 0 0 0 5 0 0 15 30 0 1 25 0 0 0

L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M 0 0 0 0 0 0 0 0 0 0 0 0 0 0

N 2 0 0 13 9 0 9.5 3.5 0 0 12.5 0 0 0 G 0 0 0 0 0 0 0 0 0 0 0 60 0 0 H 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Weighted networks


20

Weighted networks

Properties of the interbank network

In order to gain a deeper understanding of the dynamic’s of the

interbank system, we consider a range of commonly used indicators of

cohesion, centrality and distribution as aggregate network measures.

These indicators are used to investigate the statistical and structural

properties of the interbank system.

Centrality measures enable us to study the distribution of banks within

the network and determine their power, influence and control;

Cohesion measures reveal key relationships within the interbank market in

terms of connectivity,

Distance measures offer insight into the span of the network and how

different types of information may flow through the interbank market.

21

Centrality and distribution

Degree centrality:

The degree of a node is the number of edges connected

to that node.

In terms of the interbank network, this indicates the

number of other banks that a given bank has lending and

borrowing relationship with.

The greater the total degree of a bank, the higher is the

interconnectedness of the bank to other banks in the

system through interbank lending.

22


Average network degree = 2.7

BANK DEGREE IN-DEGREE

OUT-DEGREE

A 4 3 1

B 2 0 2

C 2 0 2

D 5 0 5

E 3 3 1

F 4 3 2

G 1 0 1

H 1 0 1

I 1 1 0

J 2 2 0

K 3 3 0

L 1 1 0

M 2 2 0

N 7 3 6 23


Clustering coefficient:

Measures the density of connections around a single node and

enables us to determine the proportions of nearest neighbours of a

node that are linked to each other.

A measure of connectedness between a node’s neighbours

The clustering co-efficient is used to check if a certain group of

banks transact or interacts within itself, and more importantly how

this behaviour changes over time.

A high network clustering coefficient means that any two banks

that already transact with a third bank are more likely to maintain

this relationship than to establish new connections with any other

bank in the network.

24


Average clustering

coefficient = 0.027

25

BANK CLUSTERING COEFFICIENT

A 0.167

B 0.000

C 0.000

D 0.000

E 0.000

F 0.167

G 0.000

H 0.000

I 0.000

J 0.000

K 0.000

L 0.000

M 0.000

N 0.048


Neighbouring banks that share mutual relations

are more likely to share the burden of a potential

default and are at the same time more likely to

suffer from contagion.

However, no benchmark for this measure so it’s best

to analyse it over time.

26


Betweenness centrality:

Defined as the number of shortest paths from all

vertices to all others that pass through that node.

Captures the frequency with which a given bank lies

on the shortest path between all sets of possible

bank pairs within the sample.

27


28

BANK BETWEENNESS CENTRALITY

A 23.000

B 0.900

C 0.333

D 17.167

E 6.900

F 16.467

G 0.000

H 0.000

I 0.000

J 2.333

K 6.900

L 0.000

M 1.400

N 39.600


Betweenness centrality:

Presumably, if a bank is part of many paths that connect

other banks to each other, then it is likely to have

informational or relational importance within the

networks since it is vital in connecting banks to each

other.

Captures the importance of a bank not only in the first

degree (direct) links but also in the multiple-degree

(indirect) links that connect any given pair of banks.

29


Closeness centrality:

Closeness can be regarded as a measure of how long it

will take to spread information from one node to all

other nodes sequentially

A measure of the speed with which information spreads

through the network from a specific bank

In the interbank network, this bank would facilitate the

efficient spread of liquidity, as well as the rapid spread of

shocks.

30


31

BANK CLOSENESS CENTRALITY

A 0.042

B 0.030

C 0.028

D 0.040

E 0.038

F 0.043

G 0.031

H 0.028

I 0.028

J 0.033

K 0.038

L 0.027

M 0.036

N 0.050


Strength:

Defined as the sum of a bank’s assets and liabilities.

Determine the actual weight of each node, that is,

the size of the trades through that node.

For directed network, compute in-strength and out-

strength:

A bank with high in-strength is a strong borrower, while a

bank with high out strength is a strong lender.

32


33

BANK STRENGTH OUT-STRENGTH

IN-SRENGTH

A 21.6 1 20.6

B 9.2 9.2 0

C 28.4 28.4 0

D 76 76 0

E 72.9 40 32.9

F 86.7 66 20.7

G 60 60 0

H 1 1 0

I 1 0 1

J 15.5 0 15.5

K 53.5 0 53.5

L 1 0 1

M 37.5 0 37.5

N 197.9 49.5 148.4

Cohesion and connectivity

Network density: 0.2088

An aggregate measure of connectivity, represents the

probability of any two random banks within the market

transacting with each other.

It is computed as the number of links observed in the

network at a given time divided by the total number of

possible links.

For the interbank liability network, a high density

therefore reflects a very active interbank market with

many lending relationships amongst participants.

34


Network density: 0.2088

While high network density holds the benefits of greater risk

diversification, this may not hold if the exposures exceed the level of

connectivity, thus increasing contagion risk.

The cohesion between banks that is beneficial in normal times can lead to

contagion during stressed periods.

Nevertheless, a certain level of network density must be maintained in

order to guard against the impact of contagion risk

While high density increases the network’s vulnerability to shocks,

allowing them to spread through network faster, it is possible that

depending on banks’ capital levels, the impact of the shock would be

quickly absorbed.

35


Simple measures of cohesion and connectivity:

Number of nodes

Number of links (edges)

Cohesion measures best compared across time

since there are no widely accepted benchmarks.

36

Distance measures

Average path length and network

diameter help to identify how

quickly information is spread

through an entire network.

A reduction in these indicators

would mean two things;

Increased market efficiency regards

distribution of funding or,

Increased vulnerability to contagion

risk as a sudden shock would be

transmitted through fewer banks.

37

AVERAGE PATH LENGTH

DIAMETER

2.1 4.0

Conclusion

The level of completeness and connectivity in the interbank market

may vary over short periods as market participants adjust to several

factors including their level of available funding, interest rates in the

interbank market, financial performance of banks, among others.

Further explore the network topology of the interbank market for both

secured and unsecured claims,

Determine the source and likelihood of initial shocks to the market and

study the distribution of losses.

Work on interbank network analysis should contribute to the

development of a stress testing framework for assessing systemic risk.

38

Network analysis aides

Gephi

https://gephi.org/

An interactive visualization and exploration open-source

platform for all kinds of networks and complex systems,

dynamic and hierarchical graphs.

NodeXL

http://nodexl.codeplex.com/

Open-source template for Microsoft® Excel® 2007, 2010 and

(possibly) 2013 that makes it easy to explore network graphs

39

https://gephi.org/

https://gephi.org/

https://gephi.org/

https://gephi.org/

https://gephi.org/

https://gephi.org/









REFERENCES Allen, F and Gale, D (1998), ‘Optimal financial crises’, Journal of Finance, Vol.53 (4), pages 1,245-84

Allen, F and Gale, D (2000), ‘Financial contagion’, Journal of Political Economy, Vol.108 (1), pages 1-33

Anand, K, Gai, P, Kapadia, S, Brennan, S, Willison, M (2011), ‘A network model for financial system resilience’

Babus, A (2005), ‘Contagion risk in financial networks’, Tinbergen Institute, Erasmus Universiteit Rotterdam

Canedo, J.M.D, Martinez-Jaramillo, S, ‘Financial contagion: a network model for estimating the distribution of losses for

the financial system’

De Masi, G, Iori, G, Caldarelli, G (2008), ‘The Italian interbank network: statistical properties and a simple model’,

Department of Economics, City University, London, England

Gai, P, Haldane, A and Kadapia, S (2011), ‘Complexity, concentration and contagion’

Li, S, He, J, and Zhuang, Y (2010), ‘A network model of the interbank market’

Mistrulli, P.E (2008), ‘Assessing financial contagion in the interbank market: maximum entropy versus observed

interbank lending patterns’

‘Newman, M.E.J, ‘Random graphs as models of networks’, Santa Fe Institute

Nier, E, Yang, J, Yorulmazer, T, and Alentorn, A (2008), ‘Network models and financial stability’, Working Paper No.346,

Bank of England

Sachs, A (2010), ‘Completeness, interconnectedness and distribution of interbank exposures – a parameterised analysis

of the stability of financial networks’ Deutsche Bundesbank

40

Documents

Interbank network analysis - COMESA Monetary Institute …cmi.comesa.int/.../uploads/2014/06/Interbank-network-analysis.pdf · Interbank network analysis . 2 Key Question: If one