XVA Estimates with Empirical Martingale Simulation

Wilmott Magazine, March 2022, 50-59

11 Pages Posted: 25 Oct 2021 Last revised: 16 Jan 2023

Date Written: October 28, 2021


We explore simple finite sample adjustments to simulated spot FX rates, zero bonds, forward IBORs and the numeraire to ensure the martingale asset pricing property of linear IR and FX products holds exactly with a finite number of Monte Carlo simulations. The impact on CVA, DVA, and CVA-DVA level and sensitivity Monte Carlo estimates for portfolios of uncollateralized swaps is measured for both local and global models, forward and risk neutral measures, when using pseudo and quasi random numbers. Results, for the most part, are promising/reassuring, with the largest accuracy gains obtained for in-the-money portfolios and the CVA-DVA metric.

Keywords: Monte Carlo, Option Pricing, Variance Reduction, Moment Matching, Empirical Martingale Simulation, XVA, CVA, DVA, Greeks, Quasi-Monte Carlo, Sobol' Sequences, Derivative Estimation

JEL Classification: C10, C15, C13, G13

Suggested Citation

Renzitti, Stefano and Bastani, Pouya and Sivorot, Steven, XVA Estimates with Empirical Martingale Simulation (October 28, 2021). Wilmott Magazine, March 2022, 50-59, Available at SSRN: https://ssrn.com/abstract=3948228 or http://dx.doi.org/10.2139/ssrn.3948228

Stefano Renzitti (Contact Author)

S&P Global ( email )

1066 West Hastings Street
Vancouver, British Columbia V6E 3X1

Pouya Bastani

IHS Markit ( email )

25 Ropemaker Street
4th floor Ropemaker Place
London, EC2Y 9LY
United Kingdom

Steven Sivorot

S&P Global ( email )

1066 West Hastings Street
Unit 1780
Vancouver, BC V6E 3X1
1-778-372-4537 (Phone)

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