Double Impact on CVA for CDS: Wrong-Way Risk with Stochastic Recovery

Current CVA modeling framework has ignored the impact of stochastic recovery rate. Due to the possible negative correlation between default and recovery rate, stochastic recovery rate could have a doubling effect on wrong-way risk. In the case of a payer CDS, when counterparty defaults, the CDS value could be higher due to default contagion while the recovery rate may also be lower if the economy is in a downturn. Using our recently proposed model of correlated stochastic recovery in the default time Gaussian Copula framework, we demonstrate this double impact on wrong-way risk in the CVA calculation for a payer CDS. We also present a new form of Gaussian copula that correlates both default time and recovery rate.