Valuing Credit Derivatives Using an Implied Copula Approach

by John Hull of the University of Toronto, and
Alan White of the University of Toronto

November 2006

Abstract: We present an alternative to the Gaussian copula/base correlation model for valuing CDO tranches. Instead of implying copula correlations from market prices we imply the copula itself. Our model fits the market quotes for actively traded CDO tranches exactly. It is easy to understand and is a useful tool for pricing, trading, and risk management. It enables non-standard credit derivatives, such as bespoke CDOs and CDO squareds, to be priced consistently with market quotes for tranches of standard CDOs. Contrary to some of the criticisms that have been made of the approach, we find that it is more stable than the Gaussian copula/base correlation approach. Indeed our results suggest that the spreads given by the latter approach sometimes permit arbitrage.

JEL Classification: G13.

Keywords: Credit derivatives, CDO, implied copula.

Published in: Journal of Derivatives, Vol. 14, No. 2, (Winter 2006), pp. 8-28.

Previously titled: The Perfect Copula

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Related reading: " Implied Correlations in CDO Tranches"