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Modelling Dependence for Credit Derivatives with Copulas

by Jean-Frédéric Jouanin of Credit Lyonnais,
Gregory Rapuch of Credit Lyonnais,
Gaël Riboulet of Credit Lyonnais, and
Thierry Roncalli of Credit Lyonnais

August 25, 2001

Abstract: In this paper, we address the problem of incorporating default dependency in intensity-based credit risk models. Following the works of Li [2000], Giesecke [2001] and Schönbucher and Schubert [2001], we use copulas to model the joint distribution of the default times. Two approaches are considered. The first one consists in modelling the joint survival function directly with survival copulas of default times, whereas in the second approach, copulas are used to correlate the threshold exponential random variables. We compare these two approaches and give some results about their relationships. Then we try some simulations of simple products, such as first-to-defaults. Finally, we discuss the calibration issue according to Moody's diversity score.

Keywords: Copulas, intensity models, Cox processes, Bessel processes, Moody's diversity score.

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