Efficient Estimation of Sensitivities for Counterparty Credit Risk with the Finite Difference Monte-Carlo Method

Abstract

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

CVA under Bates Model with Stochastic Default Intensity

“…In order to calculate exposure at all future time, the finite difference method uses a large portion of the grid points. It makes the PDE method computationally attractive [6]. Therefore, we will employ PDE method to find exposure.…”

“…Graaf et al (2014) [5] presented various techniques to approximate exposure for early exercise option within Black-Scholes and Heston framework. Graaf et al (2014) [6] explored the exposure profiles and CVA sensitivities for Barrier option in the context of Black-Scholes and Heston model.…”

Liquidity risk in derivatives valuation: an improved credit proxy method

“…Many recent publications on CVA, and other adjustments, focus on computing future exposures (see, for e.g. de Graaf et al 2014, Graaf et al 2016, Gregory 2015, Hofer 2016, Jain et al 2016, whereas the literature on CDS proxy methodologies is very limited.…”