Calculation of exposure profiles and sensitivities of options under the Heston and the Heston Hull-White models

Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss on a financial contract due to a default event, is one of the key elements for calculating CVA. This paper provides a backward dynamics framework for assessing exposure profiles of European, Bermudan and barrier options under the Heston and Heston Hull-White asset dynamics. We discuss the potential of the Stochastic Grid Bundling Method (SGBM), which is based on the techniques of simulation, regression and bundling (Jain and Oosterlee, Applied Mathematics and Computation, 269:412–431, 2015). By SGBM we can relatively easily compute the Potential Future Exposure (PFE) and sensitivities over the whole time horizon. Assuming independence between the default event and exposure profiles, we give here examples of calculating exposure, CVA and sensitivities for Bermudan and barrier options