A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework

by Xavier Burtschell of BNP-Paribas,
Jon Gregory - Consultant, and
Jean-Paul Laurent of Université de Lyon & BNP-Paribas

February 20, 2009

Abstract: We compare some popular CDO pricing models, related to the bottom-up approach. Dependence between default times is modelled through Gaussian, stochastic correlation, Student t, double t, Clayton and Marshall-Olkin copulas. We detail the model properties and compare the semi‐analytic pricing approach with large portfolio approximation techniques. We study the independence and perfect dependence cases and the uniqueness of base correlation. The ability of the models to fit the correlation skew observed in CDO market quotes is also assessed. Eventually, we relate CDO premiums and the distribution of conditional default probabilities which appears as a key input in the copula specification.

JEL Classification: G13, G32, C02, D46, D84, M41.

AMS Classification: 91B16, 91B28, 91B30, 60E15, 62H11.

Keywords: basket default swaps, CDOs, correlation smile, base correlation, copulas, factor models, conditional default probabilities, stochastic ordering, comonotonicity.

Published in: Journal of Derivatives, Vol. 16, No. 4, (Summer 2009), pp. 9-37.

Previously titled: A Comparative Analysis of CDO Pricing Models

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