Credit Derivative Pricing with Stochastic Volatility Models

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence, hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits finite dimensional Markovian structures. The model also accommodates a correlation structure between the stochastic volatility, default-free interest rates and credit spreads. Default free and defaultable bonds are explicitly priced and an approach for pricing credit default swaps and swaptions is presented where the credit swap rates can be approximated by defaultable bond prices with varying maturities. A sensitivity analysis capturing the impact of the model parameters including correlations and stochastic volatility, on the credit swap rate and the value of the credit swaption is also presented.