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

Decision Making in the System of Assessment and Insurance of Credit Risks

“…L., Feng, Q., Kandhai, B.D., and Oosterlee, C.W. is dedicated to the evaluation of counterparty credit risks with the help of Monte Carlo method [1,2]. Basel III regulates the changes in the capital calculation to cover the counterparty credit risk with derivative operations, repo transactions and asset securitization transactions.…”

“…Basel III regulates the changes in the capital calculation to cover the counterparty credit risk with derivative operations, repo transactions and asset securitization transactions. The document determines the approach to evaluation of this kind of risk through the CVA (Credit Value Adjustment) [1,2].Despite the significant atten tion paid tothecreditriskandsufficientpracticalandtheoreticald evelopmentof the problem of its assessment at the microlevel, the issue of comprehensive assessment of the credit risk of banking activity in RF regions still remains insufficiently studied. The urgency of the issues considered in the paper, their insufficient theoretical and methodological development and considerable importance to ensure the stability and efficiency of functioning of the national banking system conditioned the choice of the topic, goal and tasks of the studies.…”

“…The following statement is important for the first method, as in (1).If the random number  has the density of distribution ) ( y f , then the distribution of the random number is  , where…”

Computing credit valuation adjustment solving coupled PIDEs in the Bates model

“…This method is based on the direct application of the hybrid techniques to the Finite Difference Monte Carlo (FDMC) method, which was first developed by de Graaf et al [11] for the Heston model and then adapted for the Bates model by Feng [12]. First of all, an estimation of the value function V (t, S, V ) is computed through a grid of values by solving equation (2.5) by employing the Alternating Direction Implicit (ADI) method and specifically the scheme proposed by Haentjens and In't Hout [16].…”

“…These techniques have been improved through the use of stochastic grid bundling method by Jain and Oosterlee [19] and by Karlson et al [21]. An interesting approach to compute the CVA -when the Heston model is assumed -is the so called finite-difference Monte Carlo (FDMC) method, proposed by de Graaf et al [11]. Such an approach combines the finite-difference method and the Monte Carlo method to solve a partial differential equation (PDE) and to estimate the mean exposure respectively.…”