Computing XVA for American basket derivatives by Machine Learning techniques - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Computing XVA for American basket derivatives by Machine Learning techniques

Résumé

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.
Fichier principal
Vignette du fichier
2209.06485v1.pdf (262.91 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04308564 , version 1 (27-11-2023)

Identifiants

Citer

Ludovic Goudenège, Andrea Molent, Antonino Zanette. Computing XVA for American basket derivatives by Machine Learning techniques. 2022. ⟨hal-04308564⟩
27 Consultations
9 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More