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The Parareal Algorithm for American Options
[La méthode pararéelle pour les options américaines]

Author

Listed:
  • Gilles Pagès

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Olivier Pironneau

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Guillaume Sall

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

This note provides a description of the parareal method, a numerical section to assess the performance of the method for American contracts in the scalar case computed by LSMC and parallelized by parareal time decomposition with two or more levels. It contains also a convergence proof for the two levels pa- rareal Monte-Carlo method when the coarse grid solution is computed by an Euler explicit scheme with time step ∆t > δt, the time step used for the Euler scheme at the fine grid level. Hence the theorem provides a tool to analyze also the multilevel parareal method.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:hal-01320331
    Note: View the original document on HAL open archive server: https://hal.sorbonne-universite.fr/hal-01320331
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    File URL: https://hal.sorbonne-universite.fr/hal-01320331/document
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.

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