Pricing credit default swaps with bilateral counterparty risk in a reduced form model with Markov regime switching

This paper provides an intensity-based model with Markov regime switching. We assume that the default intensities depend on the economic state described by a Markov chain and that default dependence comes from common shock. We derive some closed-form expressions for the joint distribution of the default times and a pricing formula of credit default swap (CDS) with bilateral counterparty risk. We use two different approaches to obtain the closed pricing formula. We perform some numerical experiments to examine how the default intensities and the regime switching affect the CDS spread.