Identifying Systemically Important Banks in Payment Systems

Kimmo Soramäki, Founder and CEO, FNASamantha Cook, Chief Scientist, FNA

Latsis SymposiumEconomics on the moveZürich, 13 September 2012

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

• 130 out of 290 billion lent to Greece consist of Target 2 balances

Example system across this presentation: A pays B one unit and C two, B pays A one, and C pays B one

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

Agenda

• Centrality • SinkRank • Experiments• Implementation

Common measures of centrality

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 byother important nodes are more central, probability of a random process

Common centrality metrics

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) calculatedonly for “Giant Strongly Connected Component” (GSCC)

• Solution: PageRank

Pagerank

• Solves the problem with a “Damping factor” a which is used to modify the adjacency matrix (M)– Gi,j= aSi,j + (1- )/a N

• Effectively allowing the random process out of dead-ends (dangling nodes), but at the cost of introducing error

• Effect of a– =0 -> a Centrality of each node is 1/N

– =1 -> a Eigenvector Centrality

– Commonly =0.85 a is used

=0.85a

=1 (0.375, 0.375, 0.258)a

Which Measure for Payment Systems?

Network processes

• Centrality depends on network process– Trajectory : geodesic paths, paths, trails or

walks– Transmission : parallel/serial duplication or

transfer

Source: Borgatti (2004)

Distance to Sink

From B

From C

1

2

1

To A

From A

From CTo B

From A

From BTo C

• Markov chains are well-suited to model transfers along walks

• Example:

SinkRank

• SinkRank averages distances 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

SinkRanks on unweighed networks

SinkRank (weighting)

Uniform(A,B,C: 33.3% )

“Real”(A: 5% B: 90% C:5%)

Note: Node sizes scale with 1/SinkRank

PageRank(A: 37.5% B: 37.5% C:25%)

How good is it?

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

Data generation process

Based on extending Barabasi–Albert model of growth and preferential attachment

Distance from Sink vs Disruption

Highest disruption to banks whose liquidity is absorbed first (low distance to sink)

Relationship between Failure Distance and Disruption when the most central bank fails

SinkRank vs Disruption

Relationship between SinkRank and Disruption

Highest disruption by banks who absorb liquidity quickly from the system (low SinkRank)

Implementing SinkRank

Payment System Simulator

available at www.fna.fi

More information at

www.fna.fi www.fna.fi/blog

Kimmo Soramäki, D.Sc.kimmo@soramaki.netTwitter: soramaki

Discussion Paper, No. 2012-43 | September 3, 2012 | http://www.economics-ejournal.org/economics/discussionpapers/2012-43