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The presentation looks at the impact of network topology on the resilience of disturbed interbank payment systems.
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Network topology and payment system resilience
- first results
Kimmo Soramäki1
Walt Beyeler2
Morten L. Bech3
Robert J. Glass2
1Helsinki Univ. of Technology / European Central Bank
2Sandia National Laboratories
3Federal Reserve Bank of New York
Bank of Finland Simulation Seminar and Workshop
23 August 2006
The views expressed in this presentation are those of the authors and do not necessarily reflect the views of their respective institutions
2
Research problem and approach
• How does the topology of the payment network affect its resilience?
• Devise a simple model to test the impact of topology:
1. stochastic instruction arrival process2. “prototypical” topologies of interbank relationships3. simple reflexive bank behavior, and4. single disrupted bank
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• Each bank has a given level of customer deposits (Di)• Each unit of deposits has the same probability of been
transformed into a payment instruction
• where λi is the initial rate
• When a bank receives a payment its deposits increase-> the instructions arrival increases
• When a bank sends a payment its deposits decrease-> the instructions arrival decreases
1. Stochastic instruction arrival process
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2. “Prototypical” topologies of interbank relationshipsHomogeneous deposit distribution
Heterogeneous deposit distribution
lattice complete random
random scale-free
400 banks, 8*400 links
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2.1 Network statisticsaverage degree
Degreerange
average path length
lattice 8 8 6.7
random – homogeneous
8 8 3.1
complete 399 399 1
random – heterogeneous
8 1 – 19 3.1
scale-free 8 1 – 225 2.6
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2.2 Real networks…
Source: The Topology of Interbank Payment Flowshttp://www.newyorkfed.org/research/staff_reports/sr243.pdf
Fedwire has a scale-free network topology
i.e. it has a power law degree distribution, where
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3. Simple reflexive bank behavior
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
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
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4. Single disrupted bank
• An “operational incident”
• Other banks are not aware: the bank can receive, but cannot send payments
• The single bank acts as a liquidity sink. Eventually all liquidity is at the failing bank and no payments can be settled
• We examine the liquidity absorption rate and system throughput in the time period until all liquidity is at the failing bank
Example: queues in a lattice network, 10,000 nodes, low liquidity
before:
after:
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Steady state performance
Steady state performance is varies under the alternative network topologies
time
queu
e
steady state
Low liquidity
High liquidity
time
queu
es
10
0
25,000
50,000
75,000
100,000
125,000
1 10 100
1,00
0
10,0
00
100,
000
1,00
0,00
0
total liquidity
que
ues
Queues in steady state
Shorter average path length
Shorter average path length, higher degree heterogeneity
Shortest average path length
High average path length, uniform degree distribution
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0
50,000
100,000
150,000
200,000
250,000
1 10 100
1,00
0
10,0
00
100,
000
1,00
0,00
0
total liquidity
que
ues
Queues in steady state: scale free network
Highest degree heterogeneity
-> higher degree heterogeneity and a longeraverage path lengthincrease the level of queues in the steady state
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Liquidity absorption rate
The amount of liquidity absorbed by the failing bank
by each instruction arriving to the system
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0.00%
0.10%
0.20%
0.30%
0.40%
0.50%10 10
0
1,00
0
10,0
00
100,
000
1,00
0,00
0
liquidity
liq. a
bsor
ptio
n ra
te
Liquidity absorption rate
Shorter average path length
Shortest average path length
Higher degree heterogeneity, larger failing bank
High average path length, uniform degree distribution
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Liquidity absorption rate: scale free network
Highest degree heterogeneity, largest failing bank
Higher degree heterogeneity/ larger failing bank and a shorteraverage path length increase the speed of liquidity absorption
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%10 10
0
1,00
0
10,0
00
100,
000
1,00
0,00
0
liquidity
liq. a
bsor
ptio
n ra
te
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Throughput
The fraction of arriving instructions that the bank can settle in a given time interval
(the remaining being queued)
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25%
50%
75%
100%
10 100
1,00
0
10,0
00
100,
000
1,00
0,00
0
liquidity
thro
ughp
ut
Throughput
Shorter average path length
Shortest average path length
Higher degree heterogeneity, larger failing bank
High average path length, uniform degree distribution
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0%
20%
40%
60%
80%
100%
10 100
1,00
0
10,0
00
100,
000
1,00
0,00
0
liquidity
thro
ughp
ut
Highest degree heterogeneity, largest failing bank
Throughput: scale-free network
Throughput decreases with increased degree heterogeneity and the removal of larger banks
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Summary
• First investigation into the impact of topology in “payment system” type of network dynamics
• Topology matters– both for normal performance and– for performance under stress– efficient topologies are not necessarily less resilient
• Next steps– Investigate alternative times for other banks’ knowledge of failure
and failure resumption times– Impact of the existence of a market?– Perturbations in market?– Build behavior for banks
