Systemic risk in micro level the case of cheques as collateral network
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Aristotle University, Mathematics Department Master in Web Science. supported by Municipality of Veria. Systemic risk in micro level: the case of “ cheques-as-collateral ” network. Michalis Vafopoulos , j oint work with D. Soumpekas and V. Angelis 21/10/2011. outline.

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Systemic risk in micro level: the case of “ cheques-as-collateral ” network

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Aristotle University, Mathematics Department

Master in Web Science

supported by Municipality of Veria

Systemic risk in micro level: the case of “cheques-as-collateral” network


joint work with D. Soumpekas and V. Angelis



  • Financial crisis: a network explanation

  • Why networks?

  • Systemic risk and financial contagion

  • The “cheques-as-collateral” network

  • Data and model

  • Results

  • Further extensions

Financial crisis: a network explanation

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

    A reality: Regulation based on binary relations

    • Government & bank

    • Bank & customer

      and a dogma: “too big to fail”

  • Research on correlation and market risk

    (VaR-like metrics)

We cannot do…

Current risk systems cannot:

  • Predict failure cascades.

  • Account for linkages.

  • Determine counterparty losses.

Financial crisis: a network explanation

But the financial system (+info) is:

A global networked system


+ “too interconnected to fail”

How to model it?


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

Networktheory and related fields

Financial Network Analysis

Web Science

Social Network Analysis


Computer Science

Graph & Matrix Theory

Biological Network Analysis


  • Define:

  • Node (e.g. person, business)

  • 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)




Financial networks

Focused on banks, financial institutions etc.

Federal funds

Italian money market

Bech, 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

Financial Systemic risk from grass-roots

What about trying model systemic risk directly from bank customers?

Financial systemic risk (definitions)

  • 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.

The “cheques-as-collateral” network

  • Nodes: cheque issuers & recipients

  • Link ij : 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 chequesas collateral

    to working capital credit.


The model-1

(based on Martínez-Jaramillo et al., 2010).

Step 0

  • 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 0

3. 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 1

  • Calculate the sum of the defaulted exposures of failed customer i to j:

The model-4

Step 1

2. 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.


Stage 0

Number of failed nodes: 5

Decrease in total value: 17%


Stage 1

Number of failed nodes: 4

Decrease in total value: 27%


Stage 2

Number of failed nodes: 3

Decrease in total value: 38%


Stage 3

Number of failed nodes: 2

Decrease in total value: 41%


After the shock

Number of failed nodes: 14

Decrease 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

  • So, variety of hypothesis for the stage-by-stage loss function

Evaluating the systemic risk of a bank customer

  • decreasing stage-by-stage loss

  • composite loss (e.g. weight)

  • systemic risk assessment (e.g. cheque issuer)

Further extensions

  • More data and metrics

  • Model the initial shock

  • Reverse logic: business development “multiplier” for banks

  • and other sectors…

    Thank you.

    More at


Our model is based on the idea of the Systemic Risk Network Model that accounts for bank failures in the financial system (Martínez-Jaramillo et al., 2010).

Decreasing stage-by-stage loss

the total adjusted loss is calculated by weighting stage 0 loss with 0.5, stage 1 loss with 0.25 and stage 2 loss with 0.125.

composite loss (e.g. weight)

taking into account her weight in the network.

systemic risk assessment

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