Applied systemic approach in the banking sector:

financial contagion in the “cheques-as-collateral” network

Michalis Vafopoulosjoint work with D. Soumpekas

6/5/2011

Aristotle University, Mathematics Department Master in Web Science

supported by Municipality of Veria

outline

① Financial crisis: a network explanation

② Why networks? ③ Systemic risk and financial

contagion④ The “cheques-as-collateral”

network⑤ Data and model⑥ Results ⑦ Further extensions 2

Financial crisis: a network explanation

• 2007: Started from US sub-prime and disseminated rapidly to the global real economy

• Regulation based on binary relations – Government & bank– Bank & customer

• and in “too big to fail”

• Research on correlation and market risk (VaR-like metrics)

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Financial crisis: a network explanation

Current risk systems cannot:• Predict failure cascades. • Account for linkages. • Determine counterparty losses.

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Financial crisis: a network explanation

But the financial system is:

A global networked system

So,

+ “too interconnected to fail”

How to model it?Networks!

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Why networks? • Easy to model and visualize relations• Easy to calculate major statistics • The study of the Web network help us to

conclude that most of real networks are:– Self-similar (Scale-free)– Small worlds

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NETWORK THEORY

Financial Network Analysis

Biological Network Analysis

Graph & Matrix Theory

Web Science

Social Network Analysis

Computer Science

Network theory and related fields

how? • Define:

1. Node (e.g. person, business)

2. Link [directed or not] (e.g. friendship, commerce)

And if necessary:

3. Evaluation of node (e.g. score, potential)

4. Evaluation of link (weight) (e.g. trust)

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4 50.54

Federal fundsBech, M.L. and Atalay, E. (2008), “The Topology of the Federal Funds Market”. ECB Working Paper No. 986. Iori G, G de Masi, O Precup, G Gabbi and G Caldarelli (2008): “A

network analysis of the Italian overnight money market”, Journal of Economic Dynamics and Control, vol. 32(1), pages 259-278

Italian money market

Financial networksFocused on banks, financial institutions etc.

Financial Systemic risk from grass-roots

What about trying model systemic risk directly from bank customers?

Financial systemic risk• The risk of disruption to a financial

entity with spillovers to the real economy.

• The risk that critical nodes of a financial network fail disrupting linkages.

• Financial contracts with externalities.

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The “cheques-as-collateral” network

• Nodes: cheque issuers and recipients • Link ij : customer i issues cheque to customer

j• Weight of link: the fraction of the value of

cheques that customer i have issued to customer j, to the total value of cheques in euros received by the bank

Cheque recipients use their incoming cheques as collateral to working capital credit.

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Data

The model-1

Step 01. Assume a set of criteria for the

failure of every customer (c). Here it is assumed that c=50% of the total amount of the unpaid cheques that drives every customer to failure.

2. For a given “cheques-as-collateral” network, calculate the weighted adjacency matrix (W).

The model-2

Step 03. Calculate the failure threshold for every customer j:

It is assumed that this threshold remains constant in every stage k.

4. Assume a set of customers that initially fail to pay their cheques (Dk=0).

This set can be chosen by some relevant criterion. In our case, five customers with the highest weighted out-degree have been selected to collapse at stage k=0.

The model-3

Step 11. Calculate the sum of the defaulted

exposures of failed customer i to j:

The model-4

Step 12. Compare the calculated defaulted exposure failure threshold of customer j.

3. Update Dk with the failed customers.

The model-5

Step 2• Repeat Step 1 until Dk=Dk+1.

Results-1

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Stage 0 Number of failed nodes: 5Decrease in total value:

17%

Results-2

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Stage 1Number of failed nodes: 4Decrease in total value:

27%

Results-3

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Stage 2Number of failed nodes: 3Decrease in total value:

38%

Results-4

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Stage 3Number of failed nodes: 2Decrease in total value:

41%

Results-5

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After the shock

Number of failed nodes:

14Decrease in total value:

41%

Evaluating the systemic risk of a bank customer

• Assume that only a customer fails• Ceteris paribus• Calculate financial contagion• Compare to others• Weight factors like stage, sector etc

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Further extensions• More data and metrics• Model the initial shock• Reverse logic: development

multiplier

Thank you.Questions?

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