The presentation looks at the impact of network topology on the resilience of disturbed interbank payment systems.

1. Bank of Finland Simulation Seminar and Workshop
23 August 2006
Network topology
and payment system resilience
- first results
Kimmo Soramäki1
Walt Beyeler2
Morten L. Bech3
Robert J. Glass2
1
Helsinki Univ. of Technology / European Central Bank
2
3
Sandia National Laboratories
Federal Reserve Bank of New York
The views expressed in this presentation are those of the authors and do not
necessarily reflect the views of their respective institutions

2. 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 process
2. “prototypical” topologies of interbank relationships
3. simple reflexive bank behavior, and
4. single disrupted bank

3. 3
1. Stochastic instruction arrival process
• 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

4. 4
2. “Prototypical” topologies of interbank relationships
Homogeneous deposit distribution 400 banks, 8*400 links
lattice complete random
Heterogeneous deposit distribution
random scale-free

5. 5
2.1 Network statistics
average Degree average path
degree range length
lattice 8 8 6.7
random 8 8 3.1
– homogeneous
complete 399 399 1
random 8 1 – 19 3.1
– heterogeneous
scale-free 8 1 – 225 2.6

6. 6
2.2 Real networks…
Fedwire has a scale-free
network topology
i.e. it has a power law
degree distribution, where
Source: The Topology of Interbank Payment Flows
http://www.newyorkfed.org/research/staff_reports/sr243.pdf

7. 7
3. Simple reflexive bank behavior
Central bank
Payment system
4 Payment account 5 Payment account
is debited is credited
Bi Bj
6 Depositor account
3 Payment is settled is credited
or queued
Qi Bi > 0 Di Dj Qj > 0 Qj
2 Depositor account Bank i Bank i 7 Queued payment,
is debited if any, is released
1 Agent instructs
bank to send a
payment
Productive Agent Productive Agent

8. 8
Example: queues in a lattice network,
4. Single disrupted bank 10,000 nodes, low liquidity
before:
• 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 after:
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

9. 9
Steady state performance
steady state
Low liquidity
queues
queue
High liquidity
time
time
Steady state performance is varies
under the alternative network topologies

10. 10
Queues in steady state
High average path length,
uniform degree distribution 125,000
Shorter average path length, 100,000
higher degree heterogeneity
Shorter average path length 75,000
queues
Shortest average path length 50,000
25,000
0
1
10
100
1,000
10,000
1,000,000
100,000
total liquidity

11. 11
Queues in steady state: scale free network
250,000
Highest degree
heterogeneity 200,000
150,000
queues
-> higher degree
heterogeneity and a longer 100,000
average path length
increase the level of
queues in the steady state 50,000
0
1
10
100
1,000
10,000
1,000,000
100,000
total liquidity

12. 12
Liquidity absorption rate
The amount of liquidity absorbed
by the failing bank
by each instruction arriving to the system

13. 13
Liquidity absorption rate
0.50%
Higher degree heterogeneity,
0.40% larger failing bank
liq. absorption rate
0.30% Shortest average path length
0.20% Shorter average path length
High average path length,
0.10% uniform degree distribution
0.00%
10
100
1,000
10,000
100,000
1,000,000
liquidity

14. 14
Liquidity absorption rate: scale free network
5.00%
4.00% Highest degree heterogeneity,
largest failing bank
liq. absorption rate
3.00%
Higher degree heterogeneity/
2.00% larger failing bank and a shorter
average path length increase
the speed of liquidity absorption
1.00%
0.00%
10
100
1,000
100,000
1,000,000
10,000
liquidity

15. 15
Throughput
The fraction of arriving instructions
that the bank can settle
in a given time interval
(the remaining being queued)

16. 16
Throughput
100%
High average path length,
uniform degree distribution 75%
throughput
Shortest average path length
Shorter average path length 50%
Higher degree heterogeneity,
larger failing bank 25%
1,000,000
1,000
10,000
10
100
100,000
liquidity

17. 17
Throughput: scale-free network
Throughput decreases with 100%
increased degree
heterogeneity and the 80%
removal of larger banks
throughput
60%
40%
20%
Highest degree heterogeneity,
largest failing bank
0%
10
100
1,000
10,000
100,000
1,000,000
liquidity

18. 18
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