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 , vafopoulos.org j oint work with D. Soumpekas and V. Angelis 21/10/2011. outline.
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Aristotle University, Mathematics Department
Master in Web Science
supported by Municipality of Veria
joint work with D. Soumpekas and V. Angelis
A reality: Regulation based on binary relations
and a dogma: “too big to fail”
Current risk systems cannot:
But the financial system (+info) is:
A global networked system
+ “too interconnected to fail”
How to model it?
Networktheory and related fields
Financial Network Analysis
Social Network Analysis
Graph & Matrix Theory
Biological Network Analysis
And if necessary:
3. Evaluation of node (e.g. score, potential)
4. Evaluation of link (weight) (e.g. trust)
Focused on banks, financial institutions etc.
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
What about trying model systemic risk directly from bank customers?
Financial systemic risk (definitions)
Cheque recipients use their
incoming chequesas collateral
to working capital credit.
(based on Martínez-Jaramillo et al., 2010).
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).
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.
2. Compare the calculated defaulted exposure failure threshold of customer j.
3. Update Dk with the failed customers.
Number of failed nodes: 5
Decrease in total value: 17%
Number of failed nodes: 4
Decrease in total value: 27%
Number of failed nodes: 3
Decrease in total value: 38%
Number of failed nodes: 2
Decrease in total value: 41%
After the shock
Number of failed nodes: 14
Decrease in total value: 41%
More at www.vafopoulos.org
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).
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.
taking into account her weight in the network.