Journal of Computational Finance

Risk.net

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

Cornelis S. L. de Graaf, Drona Kandhai and Peter M. A. Sloot

  • We combine the finite difference method with the Monte Carlo method to obtain exposure profiles and sensitivities for computationally challenging path-dependent options.
  • This is done 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.
  • Even in the higher dimensional case, when stochastic domestic interest rate is included, we show that we can accurately compute exposures and sensitivities of discontinuous one-touch options by using a linear interpolation technique.
  • By combining the finite difference method with the Monte Carlo method, we can compute multiple option values on one grid such that exposures of portfolios can be evaluated.

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.

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