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Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach

Author

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  • Jérôme Lelong

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

Abstract

In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regression by a Wiener chaos expansion. Not only does it allow us to deal with a non Markovian setting, but it also breaks the bottleneck induced by the least square regression as the coefficients of the chaos expansion are given by scalar products on the L^2 space and can therefore be approximated by independent Monte Carlo computations. This key feature enables us to provide an embarrassingly parallel algorithm.

Suggested Citation

  • Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.
    • Handle: RePEc:hal:journl:hal-01983115
    DOI: 10.21314/JCF.2020.394
    Note: View the original document on HAL open archive server: https://hal.univ-grenoble-alpes.fr/hal-01983115v2
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    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    3. Gilles Pagès & Olivier Pironneau & Guillaume Sall, 2016. "The Parareal Algorithm for American Options [La méthode pararéelle pour les options américaines]," Post-Print hal-01320331, HAL.
    4. repec:dau:papers:123456789/4273 is not listed on IDEAS
    5. repec:dau:papers:123456789/11984 is not listed on IDEAS
    6. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    7. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    8. Doan, Viet_Dung & Gaikwad, Abhijeet & Bossy, Mireille & Baude, Françoise & Stokes-Rees, Ian, 2010. "Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 568-577.
    9. Gilles Pages & Olivier Pironneau & Guillaume Sall, 2016. "The Parareal Algorithm for American Options
      [La méthode pararéelle pour les options américaines]      ," Working Papers hal-01320331, HAL.
    10. Gilles Pag`es & Benedikt Wilbertz, 2011. "GPGPUs in computational finance: Massive parallel computing for American style options," Papers 1101.3228, arXiv.org.
    11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Henrique Guerreiro & João Guerra, 2021. "Least squares Monte Carlo methods in stochastic Volterra rough volatility models," Working Papers REM 2021/0176, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    2. Henrique Guerreiro & Jo~ao Guerra, 2021. "Least squares Monte Carlo methods in stochastic Volterra rough volatility models," Papers 2105.04511, arXiv.org.

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