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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
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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
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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
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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
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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.
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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
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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).
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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.
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The model-3
Step 11. Calculate the sum of the defaulted
exposures of failed customer i to j:
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The model-4
Step 12. Compare the calculated defaulted exposure failure threshold of customer j.
3. Update Dk with the failed customers.
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The model-5
Step 2• Repeat Step 1 until Dk=Dk+1.
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Results-1
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Stage 0 Number of failed nodes: 5Decrease in total value:
17%
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Results-2
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Stage 1Number of failed nodes: 4Decrease in total value:
27%
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Results-3
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Stage 2Number of failed nodes: 3Decrease in total value:
38%
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Results-4
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Stage 3Number of failed nodes: 2Decrease in total value:
41%
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Results-5
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After the shock
Number of failed nodes:
14Decrease in total value:
41%
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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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