Computing XVA for American basket derivatives by Machine Learning techniques

TL;DR

This paper introduces a machine learning approach using Gaussian Process Regression to efficiently compute XVA for American basket derivatives in high-dimensional settings, improving accuracy and addressing computational challenges.

Contribution

It presents a novel application of Gaussian Process Regression to calculate XVA for multi-asset American options, overcoming high-dimensional complexity.

Findings

Gaussian Process Regression effectively handles high-dimensional problems.

Numerical experiments confirm the accuracy of the proposed method.

Control variates enhance the precision of XVA estimates.

Abstract

Total value adjustment (XVA) is the change in value to be added to the price of a derivative to account for the bilateral default risk and the funding costs. In this paper, we compute such a premium for American basket derivatives whose payoff depends on multiple underlyings. In particular, in our model, those underlying are supposed to follow the multidimensional Black-Scholes stochastic model. In order to determine the XVA, we follow the approach introduced by Burgard and Kjaer \cite{burgard2010pde} and afterward applied by Arregui et al. \cite{arregui2017pde,arregui2019monte} for the one-dimensional American derivatives. The evaluation of the XVA for basket derivatives is particularly challenging as the presence of several underlings leads to a high-dimensional control problem. We tackle such an obstacle by resorting to Gaussian Process Regression, a machine learning technique that allows one to address the curse of dimensionality effectively. Moreover, the use of numerical techniques, such as control variates, turns out to be a powerful tool to improve the accuracy of the proposed methods. The paper includes the results of several numerical experiments that confirm the goodness of the proposed methodologies.