OFRwp0009_GlassermanYoung_HowLikelyContagionFinancialNetworks

5 according to the basel committee on banking

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Unformatted text preview: ence. Mark-to-market losses spread when a lender continues to extend credit, whereas a run requires withdrawal of credit. In the seminal framework of Diamond and Dybvig (1983), a run is triggered by a demand for liquidity rather than a concern about credit quality. 5 According to the Basel Committee on Banking Supervision, for example, roughly two thirds of losses attributed to counterparty credit risk were due to mark-to-market losses and only about one third of losses were due to actual defaults. See http://www.bis.org/press/p110601.htm. 4 wk pki wj pij ci wi bi Figure 1: Node i has an obligation pij to node j , a claim pkj on node k , outside assets ci , and outside ¯ ¯ Figure 1 liabilities bi , for a net worth of wi . n node i to node j , pii = 0, and a vector c = (c1 , c2 , ..., cn ) ∈ R+ where ci ≥ 0 represents the value ¯ of outside assets held by node i in addition to its claims on other nodes in the network. Typically ci consists of cash, securities, mortgages and other claims on entities outside the network. In addition each node i may have liabilities to entities outside the network; we let bi ≥ 0 denote the sum of all such liabilities of i, which we assume have equal priority with i’s liabilities to other nodes in the network. The asset side of node i’s balance sheet is given by ci + pi = b i + ¯ j =i j =i pji , and the liability side is given by ¯ pij . Its net worth is the difference ¯ pji − pi . ¯ ¯ wi = ci + (1) j =i The notation associated with a generic node i is illustrated in Figure 1. Inside the network (indicated by the dotted line), node i has an obligation pij to node j and a claim pki on node k . The figure also ¯ ¯ shows node i’s outside assets ci and outside liabilities bi . The difference between total assets and total liabilities is the node’s net worth wi . Observe that i’s net worth is unrestricted in sign; if it is nonnegative then it corresponds to the book value of i’s equity. We call this “book value” because it is based on the nominal or face value of the liabilities pji , rather than on “market” values that reflect the nodes’ ability to pay. These market ¯ values depend on other nodes’ ability to pay conditional on the realized value of their outside assets. To be specific, let each node’s outside assets be subjected to a random shock that reduces the value of its outside assets, and hence its net worth. These are shocks to “fundamentals” that propagate through the network of financial obligations. Let Xi ∈ [0, ci ] be a random shock that reduces the value of i’s outside assets from ci to ci − Xi . After the shock, i’s net worth has become wi − Xi . Let F (x1 , x2 , ..., xn ) be the joint cumulative distribution function of these shocks; we shall consider specific classes of shock distributions in the next section. (We use Xi to denote a random variable and xi to denote a particular 5 150 50 100 5 150 5 50 50 55 55 10 5 55 10 y 10 50 50 50 5 55 55 (a) Figure 2 y 10 10 5 55 10 10 10 5 50 5 55 10 10 100 y y 50 5 55 (b) Figure 2: Two network examples. Figure 3 real...
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