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Double Default Correlation

by Martijn van der Voort of Erasmus University Rotterdam & ABN AMRO

July 17, 2004

Abstract: Copula functions have become standard practice for pricing multi-name credit derivatives. Marginal default distributions are often chosen by using a simple deterministic intensity function. It is well-known that this approach only generates default time correlation and, apart from jumps due to default events, does not generate correlation between the conditional default intensities, or the conditional spreads. In this paper we consider pricing multi-name credit derivatives taking both default time correlation as well as default intensity correlation into account. This is achieved by defining two common factors, one for each type of correlation. Further, we derive a fast way to price conditional on default events or survival for the factor model. Default and survival information is translated to information on the common factor. This approach allows us to graph conditional default intensities, or conditional CDS spreads, for simulated scenarios. These simulations show that our model results in a more realistic behavior of the conditional CDS spreads as one can distinguish both credit spread correlation as well as jumps in case of correlated default events.

JEL Classification: G13, C15.

Keywords: Risk management, Credit Risk, Credit derivatives, Dependence modelling, Copulas.

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