Pricing of credit default index swap tranches with one-factor heavy-tailed copula models |
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Authors: | Dezhong Wang Svetlozar T Rachev Frank J Fabozzi |
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Institution: | 1. Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA 93106-3110, USA;2. Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and KIT, Postfach 6980, 76128 Karlsruhe, Germany;3. Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA 93106-3110, USA;4. Yale School of Management, 135 Prospect Street, Box 208200, New Haven, CT 06520-8200, USA |
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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 time-varying 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 time-varying tail-fatness parameter. Moreover, we find that the time-varying tail-fatness parameters change dramatically over a one-year period. |
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