Efficient estimation of sensitivities for counterparty credit risk with the finite difference Monte Carlo method

According to Basel III, financial institutions have to charge a credit valuation adjustment;(CVA) to account for a possible counterparty default. Calculating this measure;and its sensitivities is one of the biggest challenges in risk management. Here, we;introduce an efficient method for the estimation of CVA and its sensitivities for a;portfolio of financial derivatives. We use the finite difference Monte Carlo (FDMC);method to measure exposure profiles and consider the computationally challenging;case of foreign exchange barrier options in the context of the Black-Scholes as well as;the Heston stochastic volatility model, with and without stochastic domestic interest;rate, for a wide range of parameters. In the case of a fixed domestic interest rate, our;results show that FDMC is an accurate method compared with the semi analytic COS;method and, advantageously, can compute multiple options on one grid. In the more;general case of a stochastic domestic interest rate, we show that we can accurately;compute exposures of discontinuous one-touch options by using a linear interpolation technique as well as sensitivities with respect to initial interest rate and variance. This;paves the way for real portfolio level risk analysis.