Semi-analytical Formula for Pricing Bilateral Counterparty Risk of CDS with Correlated Credit Risks

Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump (JCIR++), and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and C A , B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and C A , B copulas show that our method performs better both in computation speed and accuracy.