Abstract : This paper presents a full study of the Total Valuation Adjustment (TVA) simulation on American derivatives. It starts form the formulation of the problem under a general BSDE framework that includes the funding issue and the default of both parties. 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 derivatives of the work presented in Crépey (2012a,b). 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 derivatives.