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

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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, 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.

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