A Generalized Contagion Credit Risk Model with Application in Pricing CDS Index Tranche

The portfolio credit risk model with contagion is one of the most important credit risk models in credit risk theory. In such a credit risk model, due to the complex dependence structure among the underlying firms, it is usually difficult to obtain the distributions for the default times of the firms. There are still seldom available closed-form formulas for the distributions of default times under more general contagion credit risk models in the existing literature. Because of this limitation, many existing study results cannot be easily applied to do empirical analysis using market data. In this paper, we develop a new generalized contagion credit risk model with regime switching. We obtain some closed-form formulas for the distributions of the kth default times and the cumulative number of defaulted firms. As an empirical example, we focus on the pricing of the credit default swap (CDS) index tranche and present its closed-form pricing formulas under the proposed model. Based on the market data, we illustrate how to calibrate the model’s parameters and provide numerical results for the prices of the CDS index tranche. Through the numerical analysis, we find that the pricing of the proposed prediction model can provide valuable reference for the market quotes for CDS index tranche series.