A Markov Chain Copula Model for Credit Default Swaps with Bilateral Counterparty Risk

Reduced-form credit risk models are widely used in pricing and hedging credit derivatives. Generating default dependency is the key element in any such model. In this article, we use Markov copulae approach to model the dependence structure of defaults between the three obligors, one is the reference entity, another is the protection seller, the other is the protection buyer(the investor), so we can consider the bilateral counterparty risk of credit default swaps(CDS). In this Markov chain copula model, we obtain the explicit formulas of the CDS premium rates C-1(T) (with unilateral counterparty risk) and C-2(T) (with bilateral counterparty risk). And then we perform some numerical experiments to analyze the difference of the fair spreads between the unilateral case and the bilateral case.