  This paper is devoted to pricing American options using Monte Carlo and the
Malliavin calculus. Unlike the majority of articles related to this topic, in
this work we will not use localization fonctions to reduce the variance. Our
method is based on expressing the conditional expectation E[f(St)/Ss] using the
Malliavin calculus without localization. Then the variance of the estimator of
E[f(St)/Ss] is reduced using closed formulas, techniques based on a
conditioning and a judicious choice of the number of simulated paths. Finally,
we perform the stopping times version of the dynamic programming algorithm to
decrease the bias. On the one hand, we will develop the Malliavin calculus
tools for exponential multi-dimensional diffusions that have deterministic and
no constant coefficients. On the other hand, we will detail various
nonparametric technics to reduce the variance. Moreover, we will test the
numerical efficiency of our method on a heterogeneous CPU/GPU multi-core
machine.
