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 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 contagion ④ The “cheques-as-collateral” network ⑤ Data and model ⑥ 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) 3

Financial crisis: a network explanation Current risk systems cannot: Predict failure cascades. Account for linkages. Determine counterparty losses. 4

Financial crisis: a network explanation But the financial system is: A global networked system So, + “too interconnected to fail” How to model it? Networks! 5

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 6

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)

Federal funds Bech, M.L. and Atalay, E. (2008), “The Topology of the Federal Funds Market”. ECB Working Paper No 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 Italian money market Financial networks Focused 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. 10

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. 11

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 (D k=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 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 D k with the failed customers.

The model-5 Step 2 Repeat Step 1 until D k =D k+1.

Results-1 18 Stage 0 Number of failed nodes: 5 Decrease in total value : 17%

Results-2 19 Stage 1 Number of failed nodes: 4 Decrease in total value : 27%

Results-3 20 Stage 2 Number of failed nodes: 3 Decrease in total value : 38%

Results-4 21 Stage 3 Number of failed nodes: 2 Decrease in total value : 41%

Results-5 22 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 23

Further extensions More data and metrics Model the initial shock Reverse logic: development multiplier Thank you. Questions? 24