This paper is devoted to pricing American options using Monte Carlo and Malliavin calculus. We develop this method on two types of models, the multidimensional exponential model with deterministic (nonconstant) volatility and the multidimensional Heston model. To obtain good numerical results, we introduce a variance reduction technique based on conditioning and a bias reduction method that relies on an appropriate choice of the number of simulated paths in the computation of the quotient of two expectations. Since our techniques are well suited to parallel implementation, our numerical experiments are performed using multicore central process unit and many-core graphic processing unit environments.