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Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

Author

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  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Ki Wai Chau

    (CWI - Centrum voor Wiskunde en Informatica - CWI - Centrum Wiskunde & Informatica - Netherlands Organisation for Scientific Research)

  • Arij Manai

    (UM - Le Mans Université)

  • Ahmed Sid-Ali

    (ULaval - Université Laval [Québec])

Abstract

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.

Suggested Citation

  • Bruno Bouchard & Ki Wai Chau & Arij Manai & Ahmed Sid-Ali, 2019. "Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view," Post-Print hal-01666399, HAL.
    • Handle: RePEc:hal:journl:hal-01666399
    DOI: 10.1051/proc/201965294
    Note: View the original document on HAL open archive server: https://hal.science/hal-01666399v2
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/4273 is not listed on IDEAS
    2. Bouchard Bruno & Tan Xiaolu & Zou Yiyi & Warin Xavier, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    3. Bruno Bouchard & Jean-François Chassagneux, 2016. "Fundamentals and Advanced Techniques in Derivatives Hedging," Post-Print hal-01348864, HAL.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Jung-Kyung Lee, 2020. "On a Free Boundary Problem for American Options Under the Generalized Black–Scholes Model," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    2. Alghalith, Moawia, 2020. "Pricing the American options: A closed-form, simple formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).

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