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Default Risk in a Network Economy

We develop a structural model of credit risk in a network economy. In particular, we are able to account for complex counterparty relationships, where one company may be indirectly affected by the credit risk of another company in the network. In this respect, we generalize Jarrow and Yu (2001) and Collin-Dufresne, Goldstein and Hugonnier (2003), but do so in the rich context of a structural form model. We provide closed form formulae for the price of risky debt and equity, which depend upon the lending/borrowing relationships in the economy. Our model applies to completely general lender/borrower relationships, including looping relationships. Our formulae can apply to cases where not only financial flows but also operations are dependent across firms. In order to achieve these results, we use queueing theory. This paper thus represents one of the first applications of queueing theory to finance.