Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Functional quantization for pricing derivatives


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