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Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods

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  • Doan, Viet_Dung
  • Gaikwad, Abhijeet
  • Bossy, Mireille
  • Baude, Françoise
  • Stokes-Rees, Ian

Abstract

In this paper we present two parallel Monte Carlo based algorithms for pricing multi-dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of continuation and exercise values. We also evaluate the performance of both the algorithms in a desktop grid environment. We show the effectiveness of the proposed approaches in a heterogeneous computing environment, and identify scalability constraints due to the algorithmic structure.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:3:p:568-577
    DOI: 10.1016/j.matcom.2010.08.005
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    References listed on IDEAS

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    1. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286, July.
    2. Ibáñez, Alfredo & Zapatero, Fernando, 2004. "Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(2), pages 253-275, June.
    3. 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.
    4. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    5. 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.
    6. Boyle, Phelim P. & Kolkiewicz, Adam W. & Tan, Ken Seng, 2003. "An improved simulation method for pricing high-dimensional American derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 315-322.
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    Cited by:

    1. J'er^ome Lelong, 2016. "Pricing American options using martingale bases," Papers 1604.03317, arXiv.org.
    2. Jérôme Lelong, 2018. "Dual pricing of American options by Wiener chaos expansion," Post-Print hal-01299819, HAL.
    3. Ledermann, Daniel & Alexander, Carol, 2012. "Further properties of random orthogonal matrix simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 56-79.
    4. Jérôme Lelong, 2016. "Dual pricing of American options by Wiener chaos expansion," Working Papers hal-01299819, HAL.
    5. Jérôme Lelong, 2020. "Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach," Post-Print hal-01983115, HAL.
    6. Calypso Herrera & Louis Paulot, 2014. "Parallel American Monte Carlo," Papers 1404.1180, arXiv.org.

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