Counterparty Credit Exposures for Interest Rate Derivatives Using the Stochastic Grid Bundling Method

Abstract

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio, is computed based on the portfolio exposure over its lifetime. Usually the future portfolio exposure is approximated using Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates, how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution.

Keywords: Bermudan Swaptions, Credit Value Adjustment (CVA), Monte Carlo Simulation, Stochastic Grid Bundling Method (SGBM), XVA

JEL Classification: C63, C61, C15