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: Suggested Citation