Bilateral counterparty risk valuation for credit default swap in a contagion model using Markov chain

The computation of the bilateral counterparty valuation adjustment for a credit default swap (CDS) contract is in effect the modeling of the default dependence among the investor, the protection seller, and the reference entity. We present a contagion model, where defaults of three parties are all driven by a common continuous-time Markov chain describing the macroeconomic conditions. We give the explicit formula for the bilateral credit valuation adjustment (CVA) of CDS and examine the effect of the regime switching on the CVA.