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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

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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

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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

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

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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

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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 6

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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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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.

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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

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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

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Data

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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).

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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.

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The model-3 Step 1 1.Calculate the sum of the defaulted exposures of failed customer i to j:

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The model-4 Step 1 2. Compare the calculated defaulted exposure failure threshold of customer j. 3. Update D k with the failed customers.

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

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

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

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

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

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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

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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

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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

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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).

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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

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

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systemic risk assessment 31

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