Functional quantization for numerics with an application to option pricing

Pagès Gilles and Printems Jacques
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Pagès Gilles: Laboratoire de Probabilités et Modèles aléatoires, CNRS UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5. & Projet MATHFI, INRIA gpa@ccr.jussieu.fr
Printems Jacques: Laboratoire d'Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Université Paris 12, 61, avenue du Général de Gaulle, F-94010 Créteil. & Projet MATHFI, INRIA printems@univ-paris12.fr

Monte Carlo Methods and Applications, 2005, vol. 11, issue 4, 407-446

Abstract: 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.

Keywords: Functional quantization; Product quantizers; Romberg extrapolation; Karhunen-Loève expansion; Brownian motion; SDE; Asian option; stochastic volatility; Heston model. (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (5)

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DOI: 10.1515/156939605777438578

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