| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: 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.
Mots Clés: Functional quantization ; Product quantizers ; Romberg extrapolation ; Karhunen-Loève expansion ; Brownian motion ; SDE ; Asian option ; stochastic volatility ; Heston model
Date: 2004-09-09
Prépublication numéro: PMA-930