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Article

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

X. Burtschell, Jonathan Gregory and Jean-Paul Laurent
The Journal of Derivatives Summer 2009, 16 (4) 9-37; DOI: https://doi.org/10.3905/JOD.2009.16.4.009
X. Burtschell
is credit derivatives proprietary trader at BNP Paribas in Paris, France.
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  • For correspondence: xavier.burtschell@bnpparibas.com
Jonathan Gregory
is an independent consultant in Guildford, U.K.
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  • For correspondence: jon.gregory@oftraining.com
Jean-Paul Laurent
is a professor at the ISFA Actuarial School, Université de Lyon, Lyon, France, and is a scientific consultant for BNP Paribas in London, and Paris, France.
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  • For correspondence: laurent.jeanpaul@free.fr
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Abstract

We compare some popular CDO pricing models, related to the bottom-up approach. Dependence between default times is modeled 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. Finally, we relate CDO premiums and the distribution of conditional default probabilities which appears as a key input in the copula specification.

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Vol. 16, Issue 4
Summer 2009
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A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework
X. Burtschell, Jonathan Gregory, Jean-Paul Laurent
The Journal of Derivatives May 2009, 16 (4) 9-37; DOI: 10.3905/JOD.2009.16.4.009

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A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework
X. Burtschell, Jonathan Gregory, Jean-Paul Laurent
The Journal of Derivatives May 2009, 16 (4) 9-37; DOI: 10.3905/JOD.2009.16.4.009
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  • Article
    • Abstract
    • SEMI-ANALYTICAL PRICING OF BASKET DEFAULT SWAPS AND CDOS
    • THE MODELS UNDER STUDY
    • ORDERING OF CDO TRANCHE PREMIUMS
    • COMPARING BASKET DEFAULT SWAPS AND CDO PREMIUMS
    • CONCLUSION
    • APPENDIX A
    • ENDNOTES
    • REFERENCES
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