CVA with Wrong Way Risk: Sensitivities, Volatility and Hedging

Abstract

We propose a CVA model capturing the wrong way risk that is not product-specific and is suitable for large-scale computations. The model is based on a doubly stochastic default process with the default intensities proxied by credit spreads. Unlike in other models, the CVA is a function of the credit spread volatility and not only of its current level. For different exposure structures, we show how credit-market correlation affects the CVA level, its sensitivities to credit and market factors, its volatility and the quality of hedging. The wrong way risk is most significant for exposures highly sensitive to the market volatility in a situation when credit spreads are at moderate levels but both the market factors and credit spreads are volatile. In such conditions, ignoring credit-market correlations results in important CVA mispricing. We show that taking into account market conditions and, in particular, credit-market correlations is essential in designing a CVA hedging strategy. While the benefits from hedging are always magnified in the situation of the wrong way risk, the right way exposure case is more delicate: only a well-designed mix of credit and market hedges can bring volatility down. Our results raise doubts on the Basel III policy of recognizing credit but not market hedges for computing the CVA volatility capital charge.