Pricing of Credit Default Index Swap Tranches with One-Factor Heavy-Tailed Copula Models

by Dezhong Wang of the University of California, Santa Barbara,
Svetlozar T. Rachev of the University of Karlsruhe & University of California, Santa Barbara, and
Frank J. Fabozzi of Yale University

February 2007

Abstract: In this paper, we provide two one-factor heavy-tailed copula models for pricing a collateralized debt obligation and credit default index swap tranches: (1) a one-factor double t distribution with fractional degrees of freedom copula model and (2) a one-factor double mixture distribution of t and Gaussian distribution copula model. A tail-fatness parameter is introduced in each model, allowing one to change the tail-fatness of the copula function continuously. Fitting our model to comprehensive market data, we find that a model with fixed tail-fatness cannot fit market data well over time. The two models that we propose are capable of fitting market data well over time when using a proper tail-fatness parameter. Moreover, we find that the tail-fatness parameters change dramatically over a one-year period.

JEL Classification: G12, G13.

Keywords: Collateralized Debt Obligation, Credit Default Swap, Credit Default Index Swap, Credit Default Index Swap Tranches.

Published in: Journal of Empirical Finance, Vol. 16, No. 2, (March 2009), pp. 201-215.

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