The Pricing of Credit Default Swaps with Counterparty Risk: Interacting Intensities Model under Regime Switching

We consider the pricing of credit default swap with counterparty risk under a regime switching model, in which the default intensities of the protection seller and the reference entity are both influenced by an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity depends on the state of the economy described by a Markov chain. We give the explicit formula for the price of credit default swap premium with counterparty risk.