On a reduced form credit risk model with common shock and regime switching

Reduced form credit risk models are important ones in credit risk theory. In such a model, certain correlated relations are constructed to represent the default dependence structure among the default intensity processes. In this paper, we introduced a reduced form credit risk model in which the default dependence structures among default intensity processes are described by the so-called common shocks with regime-switching. We derive some closed-form expressions for the joint distribution of the default times and for the pricing formulas of the basket default swaps. We also give numerical results to show the applicable aspects of the proposed model.