TY - JOUR

T1 - Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method

AU - Karlsson, Patrick

AU - Jain, Shashi

AU - Oosterlee, Cornelis W.

PY - 2016

Y1 - 2016

N2 - 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 the 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 the 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.

AB - 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 the 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 the 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.

KW - Bermudan Swaptions

KW - credit value adjustment (CVA)

KW - Monte Carlo Simulation

KW - stochastic grid bundling method (SGBM)

KW - XVA

UR - http://www.scopus.com/inward/record.url?scp=84984865038&partnerID=8YFLogxK

U2 - 10.1080/1350486X.2016.1226144

DO - 10.1080/1350486X.2016.1226144

M3 - Article

AN - SCOPUS:84984865038

VL - 23

SP - 175

EP - 196

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 3

ER -