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Aristotle University, Mathematics Department
Master in Web Science
supported by Municipality of Veria
Applied systemic approach in the banking sector:
financial contagion in the “cheques-as-collateral”
network
Michalis Vafopoulos
joint work with D. Soumpekas
6/5/2011
outline
①Financial crisis: a network explanation
②Why networks?
③Systemic risk and financial contagion
④The “cheques-as-collateral” network
⑤Data and model
⑥Results
⑦Further extensions
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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 and related fields
Web
Science
Financial
Network
Analysis
Social Network
Analysis
NETWORK
THEORY
Computer
Science
Graph & Matrix
Theory
Biological
Network
Analysis
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)
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0.54
(e.g. trust)
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Financial networks
Focused on banks, financial institutions etc.
Federal funds
Bech, M.L. and Atalay, E. (2008), “The Topology of
the Federal Funds Market”. ECB Working Paper No. 986.
Italian money market
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
• 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 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 cheques as collateral
to working capital credit.
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Data
The model-1
Step 0
1. 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 outdegree have been selected to collapse at stage k=0.
The model-3
Step 1
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.
Results-1
Stage 0
Number of failed nodes: 5
Decrease in total value: 17%
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Results-2
Stage 1
Number of failed nodes: 4
Decrease in total value: 27%
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Results-3
Stage 2
Number of failed nodes: 3
Decrease in total value: 38%
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Results-4
Stage 3
Number of failed nodes: 2
Decrease in total value: 41%
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Results-5
After the shock
Number of failed nodes: 14
Decrease in total value: 41%
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Evaluating the systemic risk of a bank customer
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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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