Functional quantization for pricing derivatives

We investigate in this paper the numerical performances of quadratic functional quantization and their applications to Finance. We emphasize the rôle played by the so-called product quantizers and the Karhunen-Loève expansion of Gaussian processes. Numerical experiments are carried out on two classical pricing problems: Asian options in a Black-Scholes model and vanilla options in a stochastic volatility Heston model. Pricing based on "crude" functional quantization is very fast and produce accurate deterministic results. When combined with a Romberg $\log$-extrapolation, it always outperforms Monte Carlo simulation for usual accuracy levels