Pricing CDS under Reduced Form Credit Risk Models with Dependent Default Risk

In this talk, we introduce some reduced form portfolio credit risk models. We show how the default intensity of a defaultable firm can be defined as the intensity of a point process. The default time of the firm is thus defined as the first jump time of the point process. The default dependence is described by the dependence of the default intensity processes. For the portfolio credit risk models, we obtain some joint distributions of the default times. By those results, we can derive some explicit pricing formulas for the CDS spreads for some portfolio credit derivatives.