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XVA PRINCIPLES, NESTED MONTE CARLO STRATEGIES, AND GPU OPTIMIZATIONS

Lokman A. Abbas-Turki, Stéphane Crépey () and Babacar Diallo
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Lokman A. Abbas-Turki: Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre-et-Marie Curie, UMR 7599, France
Stéphane Crépey: #x2020;LaMME, Université d’Evry, CNRS, Université Paris-Saclay, 91037, Evry, France
Babacar Diallo: Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre-et-Marie Curie, UMR 7599, France†LaMME, Université d’Evry, CNRS, Université Paris-Saclay, 91037, Evry, France‡Quantitative Research GMD/GMT Crédit Agricole, CIB 92160, Montrouge, France

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 06, 1-40

Abstract: We present a nested Monte Carlo (NMC) approach implemented on graphics processing units (GPUs) to X-valuation adjustments (XVAs), where X ranges over C for credit, F for funding, M for margin, and K for capital. The overall XVA suite involves five compound layers of dependence. Higher layers are launched first, and trigger nested simulations on-the-fly whenever required in order to compute an item from a lower layer. If the user is only interested in some of the XVA components, then only the sub-tree corresponding to the most outer XVA needs be processed computationally. Inner layers only need a square root number of simulation with respect to the most outer layer. Some of the layers exhibit a smaller variance. As a result, with GPUs at least, error-controlled NMC XVA computations are doable. But, although NMC is naively suited to parallelization, a GPU implementation of NMC XVA computations requires various optimizations. This is illustrated on XVA computations involving equities, interest rate, and credit derivatives, for both bilateral and central clearing XVA metrics.

Keywords: X-valuation adjustment (XVA); nested Monte Carlo (NMC); graphics processing units (GPU) (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219024918500309

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