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In Rememberance: World Trade Center (WTC)

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Factor Copulas: Totally External Defaults

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

April 8, 2005

Abstract: In this paper we address a fundamental problem of the standard one factor Gaussian Copula model. Within this standard framework a default event will have a large impact on the default probability of the survivors, through a shock in available information on the common factor. Moreover this effect is larger for defaults occurring instantaneously.

In this paper it is shown that this problem is caused by linearly combining the common factor and idiosyncratic terms. In this paper we propose an extended model, which overcomes this problem. An extra idiosyncratic term is introduced which models totally external default risk. Here one should think of default events due to fraud, or legal issues. The most noticeable default events over the last couple of years have been Enron, Worldcom and Parmalat. All of these defaulted due to totally external causes.

The occurrence of such default events do not increase the available information on the common factor driving correlated defaults.

In addition it is shown that this extended model provides a plausible explanation for the observed compound correlation smile, or equivalently, the base correlation skew. Moreover, this model requires two additional parameters with which one can control the shape of the so-called base correlation skew.

JEL Classification: G13.

Keywords: credit risk, credit derivatives, CDOs, dependence modelling, base correlation, factor copula.

Published in: Journal of Derivatives, Vol. 14, No. 3, (Spring 2007), pp. 94-102.

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