TVA on American Options

L.A. Abbas-Turki (1) , M.A. Mikou (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 EISTI - Ecole Internationale des Sciences du Traitement de l'Information

This paper presents a full study of the Total Valuation Adjustment (TVA) simulation on American options. It starts form the formulation of the problem under a general BSDE framework that includes the funding issue and the default of both counterparties. It finishes by giving a benchmark Nested Monte Carlo algorithm and discusses an appropriate implementation that provides accurate results within a minute simulation on Graphic Processing Units (GPUs). From a theoretical point of view, this paper can be considered as the extension to American options of the work presented on both papers Crépey (2012a) and Crépey (2012b). Regarding the algorithmic part, our study uses convergence rates developed in Newey (1997) as well as similar ideas to the one presented in Gordy and Juneja (2010) and it goes beyond the square Monte Carlo algorithm detailed in Abbas-Turki et al. (2014) for European options.

Mots clés: BSDE; TVA; GPU; Nested Monte Carlo; American options

Domaines: Probabilités [math.PR]

L.A. Abbas-Turki, M.A. Mikou. TVA on American Options. 2015. ⟨hal-01142874v1⟩