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Functional quantization for numerics with an application to option pricing

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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)

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.

Suggested Citation

  • Pagès Gilles & Printems Jacques, 2005. "Functional quantization for numerics with an application to option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 11(4), pages 407-446, December.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:4:p:407-446:n:6
    DOI: 10.1515/156939605777438578
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    References listed on IDEAS

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    1. Delattre Sylvain & Graf Siegfried & Luschgy Harald & Pagès Gilles, 2004. "Quantization of probability distributions under norm-based distortion measures," Statistics & Risk Modeling, De Gruyter, vol. 22(4), pages 261-282, April.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    1. repec:hal:wpaper:hal-03902513 is not listed on IDEAS
    2. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org, revised Dec 2024.
    3. Giacomo Bormetti & Giorgia Callegaro & Giulia Livieri & Andrea Pallavicini, 2015. "A backward Monte Carlo approach to exotic option pricing," Papers 1511.00848, arXiv.org.
    4. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03902513, HAL.
    5. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Post-Print hal-03902513, HAL.

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