An Extension of Davis and Lo’s Contagion Model

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An Extension of Davis and Lo’s Contagion Model

by Didier Rullièrey of the Université de Lyon, and
Diana Dorobantu of Université Lyon 1

April 10, 2009

Abstract: The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo’s infectious default model. We consider an economy of n firms which may default directly or may be infected by another defaulting firm (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessary independent Bernoulli-type random variables. Moreover, several contaminations could be necessary to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults.

Keywords: credit risk, contagion model, dependent defaults, default distribution, exchangeability.

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