IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01320331.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.sorbonne-universite.fr/hal-01320331/document
    Download Restriction: no
    ---><---

    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. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    2. Work, James & Hauer, Grant & Luckert, M.K. (Marty), 2018. "What ethanol prices would induce growers to switch from agriculture to poplar in Alberta? A multiple options approach," Journal of Forest Economics, Elsevier, vol. 33(C), pages 51-62.
    3. Kathrin Glau & Ricardo Pachon & Christian Potz, 2019. "Speed-up credit exposure calculations for pricing and risk management," Papers 1912.01280, arXiv.org.
    4. Dong, Wenfeng & Kang, Boda, 2019. "Analysis of a multiple year gas sales agreement with make-up, carry-forward and indexation," Energy Economics, Elsevier, vol. 79(C), pages 76-96.
    5. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    6. Gabriel J Power & Charli D. Tandja M. & Josée Bastien & Philippe Grégoire, 2015. "Measuring infrastructure investment option value," Journal of Risk Finance, Emerald Group Publishing, vol. 16(1), pages 49-72, January.
    7. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    8. Mo, Jian-Lei & Schleich, Joachim & Zhu, Lei & Fan, Ying, 2015. "Delaying the introduction of emissions trading systems—Implications for power plant investment and operation from a multi-stage decision model," Energy Economics, Elsevier, vol. 52(PB), pages 255-264.
    9. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    10. Xuemei Gao & Dongya Deng & Yue Shan, 2014. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-6, April.
    11. Marcelo G. Figueroa, 2006. "Pricing Multiple Interruptible-Swing Contracts," Birkbeck Working Papers in Economics and Finance 0606, Birkbeck, Department of Economics, Mathematics & Statistics.
    12. Abdullah Almansour & Margaret Insley, 2016. "The Impact of Stochastic Extraction Cost on the Value of an Exhaustible Resource: An Application to the Alberta Oil Sands," The Energy Journal, , vol. 37(2), pages 61-88, April.
    13. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    14. Jungmin An & Dong-Kwan Kim & Jinyeong Lee & Sung-Kwan Joo, 2021. "Least Squares Monte Carlo Simulation-Based Decision-Making Method for Photovoltaic Investment in Korea," Sustainability, MDPI, vol. 13(19), pages 1-14, September.
    15. Chi H. Truong, 2014. "A Two Factor Model for Water Prices and Its Implications for Evaluating Real Options and Other Water Price Derivatives," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 62(1), pages 23-45, March.
    16. Piotr Komański & Oskar Sokoliński, 2015. "Least-Squares Monte Carlo Simulation for Time Value of Options and Guarantees Calculation," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 41.
    17. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    18. Zineb El Filali Ech-Chafiq & Pierre Henry-Labordere & Jérôme Lelong, 2021. "Pricing Bermudan options using regression trees/random forests," Working Papers hal-03436046, HAL.
    19. Joseph Y. J. Chow & Amelia C. Regan, 2011. "Real Option Pricing of Network Design Investments," Transportation Science, INFORMS, vol. 45(1), pages 50-63, February.
    20. repec:hum:wpaper:sfb649dp2006-051 is not listed on IDEAS
    21. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01320331. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.