We investigate in this paper the numerical performances of quadratic functional quantization with some applications to Finance. We emphasize the rôle played by the so-called product quantizers and the Karhunen-Loève expansion of Gaussian processes, in particular the Brownian motion. We show how to build some efficient functional quantizers for Brownian diffusions. We propose a quadrature formula based on a Romberg log-extrapolation of “crude” functional quantization which speeds up significantly the method. Numerical experiments are carried out on two European option pricing problems: vanilla and Asian Call options in a Heston stochastic volatility model. It suggests that functional quantization is a very efficient integration method for various path-dependent functionals of a diffusion processes: it produces deterministic results which outperforms Monte Carlo simulation for usual accuracy levels. | 
