Using Distortions of Copulas to Price Synthetic CDOs

by Glenis Crane of the University of Adelaide, and
John van der Hoek of the University of Adelaide

May 2007

Abstract: This paper uses distortions of the bivariate Gaussian copula to produce a heavy tail for expected portfolio loss distribution in the context of synthetic Collateralized Debt Obligations (CDOs). We demonstrate that when the distorted copulas are used within the JP Morgan CDO pricing formula, as an example, we can simulate quite realistic tranche prices. Furthermore, we need only one dependence parameter for the entire portfolio instead of one per tranche. This method may allow practitioners to price CDOs more accurately than with other versions of the Gaussian copula and with fewer correlation parameters.

Keywords: copula functions, CDOs, transformations.

Published in: Insurance: Mathematics and Economics, Vol. 42, No. 3, (June 2008), pp. 903-908.

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