NEW DIRECTIONS FOR UNDERSTANDING SYSTEMIC RISK Federal Reserve Bank of New York and The National Academy Of Sciences New York, May 18-19, 2006 Contagion,

NEW DIRECTIONS FOR UNDERSTANDING SYSTEMIC RISK

Federal Reserve Bank of New York and The National Academy Of Sciences

New York, May 18-19, 2006

Contagion, Cascades and Disruptions to the Interbank

Payment System

The views expressed in this presentation do not necessarily reflect those of

the Federal Reserve Bank of New York or the Federal Reserve System

The National Infrastructure Simulation and Analysis Center (NISAC) is a program under the

Department of Homeland Security’s (DHS) Preparedness Directorate.

Morten L. Bech

Federal Reserve Bank of New York

Walter E. Beyeler

Sandia National

Laboratories

Robert J. Glass

Sandia National

Laboratories

Kimmo Soramäki

Helsinki Technical

University

The Big Picture

Complex, Adaptive System

financial markets

clearing and settlement

central bank

markets for goods and services

financial markets

clearing and settlement

central bank

markets for goods and services

Primer on Interbank Payment System

other infrastructures

bank i bank j 7600 participants

Federal Reserve - bank of banks

Max day = 800,000 payments worth $2.9 trillion

Turnover = US GDP every six business days

markets

Large-value, time-critical payments

Real Time Gross Settlement (RTGS) system

Fed provides intraday credit for a fee

Fedwire

Lower ManhattanSeptember 15, 2001Source: Space I maging

Verizon

FRBNY

Lower ManhattanSeptember 15, 2001Source: Space I maging

Verizon

FRBNY

A Break Down in Coordination

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4 5 6 7 10 11 12 13 14 17 18 19 20 21

Benchmark

Coefficient

September 2001

Source: Federal Reserve Bank of New York

Slope Reaction Function

Slope of Reaction Function of Payments Sent to Payments Received: Fixed-Effects Tobit Model

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4 5 6 7 10 11 12 13 14 17 18 19 20 21

Benchmark

Coefficient

September 2001




t tPaymentsSent Payments Received t

McAndrews and Potter (2002)

¯

The Intraday Liquidity Management Game

Bank B

Morning Afternoon

Morning 0, 0 F, D

Ba

nk A

Afternoon D, F D, D

Bank B

Morning Afternoon

Morning 0, 0 3, 4

Ba

nk A

Afternoon 4, 3 4, 4

Bank B

Morning Afternoon

Morning 0, 0 4, 3

Ba

nk A

Afternoon 3, 4 3, 3

F < D

F > D

Fee F charged by central bank for overdrafts

Total cost = 0 (FIRST BEST)

Total cost = 0 or (6)

Stag Hunt

Time is money (also intraday) so delay is costly. The cost is D > 0 per dollar

Rational players are pulled in one direction by considerations of mutual benefit and in the other by considerations of personal risk

Adjustment following Wide-Scale Disruption

10.90.80.70.60.50.40.30.20.10

Share of Banks Playing Afternoon

-1 * Potential

Liq

uid

ity expen

sive relative to

delayin

g

F = D

D < F< 2D

F = 2D

F > 2D

Share of banks hit by disruption / holding back payments

Po

ten

tia

l

F = 2D

F < D Liq

uid

ity cheap

relative to

delayin

g

Heterogeneous Banking Sector

10.90.80.70.60.50.40.30.20.10

Share of Small Banks

-1 * Potential

Large bank not affected

Large bank affected

Po

ten

tia

l

Share of banks hit by disruption / holding back payments

Large bank not affected

Large bank affected

Po

ten

tia

l

Network Topology of Payment Flow

Research Goals

1. Evaluate the actual network topology of interbank payment flows through analysis of Fedwire transaction data

2. Build a parsimonious agent based model for payment systems that honors network topology

3. Evaluate response of payment systems to shocks and the possibility of cascading failure

Network Topology after 9/11Fedwire’s CoreFedwire’s Core

All Commercial BanksAll Commercial Banks>6600 nodes, 70,000 links>6600 nodes, 70,000 links

GIN GOUT

DC

GSCC

Tendril

GWCCTube

Network Components

GSSC Dominates

•78% nodes

•90% edges

•92% transfers

•90% value

78% nodes78% nodes12%12% 8%8%

Out-Degree Distribution

Number of Nodes in GSCC

Sept 11th

G oodFriday

T hanksg iv ingFriday

C hrism asEv e

4.5

5.0

5.5

6.0

Tho

usan

ds

Apr2001

M ay Jun Ju l Aug Sep O ct N ov D ec Jan2002

Feb M ar Apr

N um ber o f N odes in G SC CN on-9 /11 M ean +/- S t. D ev

Connectivity

Sept 11thG oodFriday0.26

0.28

0.30

0.32

0.34

Per

cent

Apr2001


Feb M ar Apr

C onnectiv ityN on-9 /11 M ean +/- S t. D ev

Average Path Length

Sept 11th

G oodFriday

T hanksg iv ingFriday

C hrism asEv e

2.55

2.60

2.65

2.70

2.75

2.80

Apr2001


Feb M ar Apr

Av erge P a th Leng thN on-9 /11 M ean +/- S t. D ev

9/11

90

95

100

105

Inde

x

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21September 2001

Nodes Aveage Path LengthConnectivity Reciprocity

Note: 100 = September 10th, 2001.

Structure Behavior

90

95

100

105

Inde

x

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

September 2001

Nodes Aveage Path LengthConnectivity Reciprocity

Note: 100 = September 10th, 2001.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4 5 6 7 10 11 12 13 14 17 18 19 20 21

Benchmark

Coefficient

September 2001




0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

4 5 6 7 10 11 12 13 14 17 18 19 20 21

Benchmark

Coefficient

September 2001




•Perhaps Switch Between the Two with Morten Perhaps Switch Between the Two with Morten Animation MagicAnimation Magic

Research Goals




Bank i Bank i

Payment system

1 Agent instructs bank to send a payment

2 Depositor account is debited

Di Dj

5 Payment account is credited

4 Payment account is debited

Productive Agent Productive Agent

Liquidity

Market

6 Depositor account is credited

Qi

3 Payment is settled or queued

Bi > 0 Qj

7 Queued payment, if any, is released

Qj > 0

Bi Bj

Central bank

Payment Physics Model

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

PaymentSystem

When liquidity is high payments are submitted promptly and banks process payments independently of each other

Instructions Payments

Summed over the network, instructions arrive at a steady rate

Influence of Liquidity

Liquidity

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

5 5 0 0 5 7 0 0 5 9 0 0 6 1 0 0

Instructions

Pay

men

ts

5 5 0 0

5 6 0 0

5 7 0 0

5 8 0 0

5 9 0 0

6 0 0 0

6 1 0 0

5 5 0 0 5 7 0 0 5 9 0 0 6 1 0 0

Instructions

Pay

men

ts

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

5 5 0 0 5 7 0 0 5 9 0 0 6 1 0 0

Instructions

Pay

men

ts

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

Reducing liquidity leads to episodes of congestion when queues build, and cascades of settlement activity when incoming payments allow banks to work off queues. Payment processing becomes coupled across the network

PaymentSystem

Instructions Payments


0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

1 E -0 4

0 .0 0 1

0 .0 1

0 .1

1

1 1 0 1 0 0 1 0 0 0 1 0 0 0 0

Cascade Length

Fre

qu

ency

1

1

Liquidity

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

5 5 0 0 5 7 0 0 5 9 0 0 6 1 0 0

Instructions

Pay

men

ts

PaymentSystem

Instructions Payments0

5000

10000

15000

20000

0 500 1000 1500 2000

Period

Num

ber o

f Ins

truct

ions

At very low liquidity payments are controlled by internal dynamics. Settlement cascades are larger and can pass through the same bank numerous times


1 E -0 4

0 .0 0 1

0 .0 1

0 .1

1

1 1 0 1 0 0 1 0 0 0 1 0 0 0 0

Cascade Length

Fre

quen

cy

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

Liquidity

1

1

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

5 5 0 0 5 7 0 0 5 9 0 0 6 1 0 0

Instructions

Pay

men

ts

PaymentSystem

Instructions Payments0

5000

10000

15000

20000

0 500 1000 1500 2000

Period

Num

ber o

f Ins

truct

ions

A liquidity market substantially reduces congestion using only a small fraction (e.g. 2%) of payment-driven flow

Influence of Market

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

1 E -0 4

0 .0 0 1

0 .0 1

0 .1

1

1 1 0 1 0 0 1 0 0 0 1 0 0 0 0

Cascade Length

Freq

uenc

y

0

2 0 0 0

4 0 0 0

6 0 0 0

8 0 0 0

1 0 0 0 0

1 2 0 0 0

1 4 0 0 0

1 6 0 0 0

1 8 0 0 0

2 0 0 0 0

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

Time

Liquidity

Market

Research Goals




Ongoing Disruption Analyses

0

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0

Simulation Period

Nu

mb

er

of

Paym

en

ts

0 .0 E +0 0

5 .0 E +0 3

1 .0 E +0 4

1 .5 E +0 4

2 .0 E +0 4

2 .5 E +0 4

3 .0 E +0 4

3 .5 E +0 4

4 .0 E +0 4

4 .5 E +0 4

5 .0 E +0 4

1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0

Simulation Period

Valu

e o

f Q

ueu

ed

Paym

en

ts

Disruption of a bank creates a liquidity sink in the system

Period of Disruption


System throughput can be rapidly degraded

0

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

3 5 0 0 0

4 0 0 0 0

3 0 0 0 5 0 0 0 7 0 0 0 9 0 0 0 1 1 0 0 0 1 3 0 0 0 1 5 0 0 0

Simulation PeriodV

alu

e o

f Q

ueu

ed P

aym

ents

5 0 0 0

5 2 0 0

5 4 0 0

5 6 0 0

5 8 0 0

6 0 0 0

6 2 0 0

6 4 0 0

6 6 0 0

6 8 0 0

7 0 0 0

3 0 0 0 5 0 0 0 7 0 0 0 9 0 0 0 1 1 0 0 0 1 3 0 0 0 1 5 0 0 0

Simulation Period

Nu

mb

er o

f P

aym

ents

Disruptions to liquidity market represented as decreased conductance

Queues build; system becomes increasingly congested; recovery quickly

follows restoration



What we’re learned

• Payment system participants have learned to coordinate their activities, and this coordination can be re-established after massive disruption

• Payment flows, like many other networks, follow a scale-free distribution

• Performance is a function of both topology and behavior – neither factor alone is enough to evaluate robustness

• Liquidity limits can lead to congestion and a deterioration of throughput, but a shift in behavior is evidently needed to understand responses to disruption

• System performance can be greatly improved by moving small amounts of liquidity to the places where it’s needed

• Collaboration among researches with different backgrounds helps bring new theoretical perspectives to real problems, and helps shape theoretical development to practical ends

Next steps

• Intraday analysis of network topology – How does it get built? Over what time scales do banks manage liquidity? Are there discernable behavioral modes (e.g. early/late settlement) or triggers (e.g.

settlement of market transactions)?

• Long-term network dynamics (e.g. changes in TARGET topology with integration)

• Disruption/recovery behavior of simple model, including a central bank• Adaptation of decision process, including market participation, to minimize cost

(ongoing). How is cooperative behavior established and maintained? How might it be disrupted, restored, through institutions’ policies and reactions?

• Modeling the processes that drive payment flows (banks’ and customer investments, market movements, etc.) to: introduce plausible correlations and other structure on the payment instruction

stream explore the feedbacks between payment system disruptions and the economy

Documents

NEW DIRECTIONS FOR UNDERSTANDING SYSTEMIC RISK Federal Reserve Bank of New York and The National Academy Of Sciences New York, May 18-19, 2006 Contagion,