Pricing of credit default index swap tranches with one-factor heavy-tailed copula models

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.