  We investigate in this paper an alternative method to simulation based
recursive importance sampling procedure to estimate the optimal change of
measure for Monte Carlo simulations. We propose an algorithm which combines
(vector and functional) optimal quantization with Newton-Raphson zero search
procedure. Our approach can be seen as a robust and automatic deterministic
counterpart of recursive importance sampling by means of stochastic
approximation algorithm which, in practice, may require tuning and a good
knowledge of the payoff function in practice. Moreover, unlike recursive
importance sampling procedures, the proposed methodology does not rely on
simulations so it is quite generic and can come along on the top of Monte Carlo
simulations. We first emphasize on the consistency of quantization for
designing an importance sampling algorithm for both multi-dimensional
distributions and diffusion processes. We show that the induced error on the
optimal change of measure is controlled by the mean quantization error. We
illustrate the effectiveness of our algorithm by pricing several options in a
multi-dimensional and infinite dimensional framework.
