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
Andrea Molent: Università degli Studi di Udine - University of Udine [Italie]
Antonino Zanette: MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris

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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: Control variates; Basket option; Gaussian process regression; XVA; American options; Transaction costs; Greeks; Hedging (search for similar items in EconPapers)
Date: 2025-08-08
Note: View the original document on HAL open archive server: https://hal.science/hal-05421581v1
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Published in Computational Management Science, 2025, 22, pp.541 - 569. ⟨10.1007/s10287-025-00540-7⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05421581

DOI: 10.1007/s10287-025-00540-7

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