Systemic risk in micro level: the case of “cheques-as-collateral” network Michalis Vafopoulos, vafopoulos.org joint work with D. Soumpekas and V. Angelis 21/10/2011 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 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) 3

We cannot do… Current risk systems cannot: Predict failure cascades. Account for linkages. Determine counterparty losses. 4

Financial crisis: a network explanation But the financial system (+info) 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 (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. 10

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 cheques as collateral to working capital credit. 11

Data

The model-1 (based on Martínez-Jaramillo et al., 2010). 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%

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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 So, variety of hypothesis for the stage- by-stage loss function 24

Evaluating the systemic risk of a bank customer 1.decreasing stage-by-stage loss 2.composite loss (e.g. weight) 3.systemic risk assessment (e.g. cheque issuer) 25

Further extensions More data and metrics Model the initial shock Reverse logic: business development “multiplier” for banks and other sectors… Thank you. More at Questions? 26

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 29 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

composite loss (e.g. weight) 30 taking into account her weight in the network.

systemic risk assessment 31