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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board Member: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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CiteScore 2016: 0.70

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Volume 11, Issue 4 (Dec 2005)


Functional quantization for numerics with an application to option pricing

Gilles Pagès
  • 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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jacques Printems
  • 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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

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.

Key Words: Functional quantization,; Product quantizers,; Romberg extrapolation,; Karhunen-Loève expansion,; Brownian motion,; SDE,; Asian option,; stochastic volatility,; Heston model.

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Published Online:

Published in Print: 2005-12-01

Citation Information: Monte Carlo Methods and Applications mcma, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/156939605777438578.

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