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Computing XVA for American basket derivatives by machine learning techniques

Ludovic Goudenège (), Andrea Molent () and Antonino Zanette ()
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Ludovic Goudenège: Université Paris-Saclay Évry
Andrea Molent: Università degli Studi di Udine
Antonino Zanette: Università degli Studi di Udine

Computational Management Science, 2025, vol. 22, issue 2, No 6, 33 pages

Abstract: 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 underlyings 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 in SSRN Electronic J 7:1–19, 2010) and afterward applied by (Arregui et al. in Appl Math Comput 308:31–53, 2017), (Arregui et al. in Int J Comput Math 96:2157–2176, 2019) 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.

Keywords: XVA; Gaussian process regression; Basket option; Control variates (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10287-025-00540-7

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