Presentation held at the Latsis Symposium at ETH on 13 September 2012

1. Latsis Symposium
Economics on the move
Zürich, 13 September 2012
Identifying Systemically
Important Banks in Payment
Systems
Kimmo Soramäki, Founder and CEO, FNA
Samantha Cook, Chief Scientist, FNA

3. Interbank Payment Systems
• Provide the backbone of all
economic transactions
• Banks settle claims arising from
customers transfers, own
securities/FX trades and liquidity
management
• Target 2 settled 839 trillion in
2010
Example system across this
• 130 out of 290 billion lent to presentation: A pays B one
Greece consist of Target 2 unit and C two, B pays A one,
balances and C pays B one

4. Systemic Risk in Payment Systems
• Credit risk has been virtually eliminated by system
design (real-time gross settlement)
• Liquidity risk remains
– “Congestion”
– “Liquidity Dislocation”
• Trigger may be
– Operational/IT event
– Liquidity event
– Solvency event
• Time scale = intraday

5. Agenda
• Centrality
• SinkRank
• Experiments
• Implementation

6. Common measures of centrality

7. Common centrality metrics
Degree: number of links
Closeness: distance to other
nodes via shortest paths
Betweenness: number of shortest
paths going through the node
Eigenvector: nodes that are linked by
other important nodes are more
central, probability of a random process

8. Eigenvector Centrality
• Eigenvector centrality (EVC) vector, v, is given by
– vP=v , where P is the transition matrix of an adjacency matrix M
– v is also the eigenvector of the largest eigenvalue of P (or M)
• Problem: EVC can be
(meaningfully) calculated
only for “Giant Strongly
Connected Component”
(GSCC)
• Solution: PageRank

9. Pagerank
• Solves the problem with a “Damping factor” which is used to
modify the adjacency matrix (M)
– Gi,j= Si,j
• Effectively allowing the random process out of dead-ends (dangling
nodes), but at the cost of introducing error
• Effect of
– Centrality of each node is 1/N
– Eigenvector Centrality
– Commonly is used

10. Which Measure for Payment Systems?

11. Network processes
• Centrality depends on network process
– Trajectory : geodesic paths, paths, trails or walks
– Transmission : parallel/serial duplication or transfer
Source: Borgatti (2004)

12. Distance to Sink
• Markov chains are well-suited to model transfers along walks
• Example:
From B 1
To A
From C 2
From A
To B
From C 1
From A
To C
From B

13. SinkRank
SinkRanks on unweighed
• SinkRank averages distances networks
to sink into a single metric for
the sink
• We need an assumption on
the distribution of liquidity in
the network
– Asssume uniform ->
unweighted average
– Estimate distribution ->
PageRank weighted average
– Use real distribution ->
Average using real distribution as
weights

14. SinkRank (weighting)
Uniform PageRank “Real”
(A,B,C: 33.3% ) (A: 37.5% B: 37.5% C:25%) (A: 5% B: 90% C:5%)
Note: Node sizes scale with 1/SinkRank

15. How good is it?

16. Experiments
• Design issues
– Real vs artificial networks?
– Real vs simulated failures?
– How to measure disruption?
• Approach taken
1. Create artificial data with close resemblance to the US Fedwire
system (Soramäki et al 2007)
2. Simulate failure of a bank: the bank can only receive but not send
any payments for the whole day
3. Measure “liquidity dislocation” and “congestion” by non-failing
banks
4. Correlate them (the “disruption”) with SinkRank of the failing
bank

17. Data generation process
Based on extending Barabasi–
Albert model of growth and
preferential attachment

18. Distance from Sink vs Disruption
Relationship between
Failure Distance and
Disruption when the most
central bank fails
Highest disruption to
banks whose liquidity is
absorbed first (low
distance to sink)

19. SinkRank vs Disruption
Relationship between
SinkRank and Disruption
Highest disruption by
banks who absorb
liquidity quickly from the
system (low SinkRank)

20. Implementing SinkRank

21. Payment System Simulator
available at www.fna.fi

22. More information at
www.fna.fi www.fna.fi/blog
Kimmo Soramäki, D.Sc.
kimmo@soramaki.net
Twitter: soramaki
Discussion Paper, No. 2012-43 | September 3, 2012 |
http://www.economics-ejournal.org/economics/discussionpapers/2012-43