Abstract
In this paper, we consider a portfolio credit risk model with the thinning-dependence structure under the case with regime switching and the one with no regime switching. We obtain the explicit expressions for the copulas of the default times. Based on the quotation convention of CDS index tranches, we derive some closed-form expressions for the pricing formulas for the CDS index tranche via the copulas and the marginal distribution functions of the default times. As an empirical example, we consider the pricing of the CDX NA IG Series 25. We demonstrate how the model parameter can be calibrated based on market data and how the numerical results can be calculated via the proposed pricing formulas. Compared to the empirical results under the pricing model with some commonly used copulas, such as the Clayton copula, the Gumbel copula, and the Frank copula, we find that the proposed pricing model with regime switching can provide a valuable reference for the market quotes for the CDX NA IG Series 25.
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