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This paper is devoted to the simulation of the Credit Valuation Adjustment (CVA) using a pure Monte Carlo technique with Malliavin calculus (MCM). The procedure presented is based on a general theoretical framework that includes a large number of models as well as various contracts, and allows both the computation of CVA and its sensitivity with respect to the different assets. Moreover, we provide the expression of the backward conditional density of assets vector that can be simulated off-line in order to reduce the variance of the CVA estimator. Using the suitability of MCM to parallel architectures and thus to a Graphic Processing Unit (GPU) implementation, we show that the results obtained are accurate once a sufficient number of trajectories is simulated. Both complexity and accuracy are studied for MCM and regression methods and are compared to the square Monte Carlo benchmark.

International audience; The aim of this paper is the efficient use of CPU and GPU clusters for a general path-dependent exotic European pricing, and their comparison in terms of speed and energy consumption. To reach our goal, we propose a parallel random number generator which is well suited to the parallelization paradigm, then, we implement a multidimensional Asian contract as a benchmark using g++/OpenMP/OpenMPI on CPUs and CUDA-nvcc/OpenMPI on GPUs. Finally, we give the detailed results of the two architectures for different size problems using 1-16 GPUs and 1-256 dual-core CPUs.