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Credit Risk in a Network Economy

IMD, CH-1001 Lausanne, Switzerland
School of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711
cossin{at}imd.ch
hschellhorn{at}yahoo.com

We develop a structural model of credit risk in a network economy, where any firm can lend to any other firm, so that each firm is subject to counterparty risk either from direct borrowers or from remote firms in the network. This model takes into account the role of each firm's cash management. We show that we can obtain a semiclosed form formula for the price of debt and equity when cash accounts are buffers to bankruptcy risk. As in other structural models, the strategic bankruptcy decision of shareholders drives credit spreads, and differentiates debt from equity. Cash-flow risk also causes credit-risk interdependencies between firms. Our model applies to the case where not only financial flows but also operations are dependent across firms. We use queueing theory to obtain our semiclosed form formulae in steady state. We perform a simplified implementation of our model to the U.S. automotive industry, and show how we infer the impact on a supplier's credit spreads of revenue changes in a manufacturer or even in a large car dealer. We also obtain prices for first-to-default and second-to-default basket credit default swaps.

Key Words: credit risk; contagion; queueing networks
History: Received: March 14, 2005;