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Distributed Least-Squares Monte Carlo for American Option Pricing

Author

Listed:
  • Lu Xiong

    (Department of Mathematical Sciences, College of Basic and Applied Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA)

  • Jiyao Luo

    (Department of Mathematical Sciences, College of Basic and Applied Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA)

  • Hanna Vise

    (Department of Mathematical Sciences, College of Basic and Applied Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA)

  • Madison White

    (Department of Mathematical Sciences, College of Basic and Applied Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA)

Abstract

Option pricing is an important research field in financial markets, and the American option is a common financial derivative. Fast and accurate pricing solutions are critical to the stability and development of the market. Computational techniques, especially the least squares Monte Carlo (LSMC) method, have been broadly used in optimizing the pricing algorithm. This paper discusses the application of distributed computing technology to enhance the LSMC in American option pricing. Although parallel computing has been used to improve the LSMC method, this paper is the first to explore distributed computing technology for LSMC enhancement. Compared with parallel computing, distributed computing has several advantages, including reducing the computational complexity by the “divide and conquer” method, avoiding the complicated matrix transformation, and improving data privacy as well as security. Moreover, LSMC is suitable for distributed computing because the price paths can be simulated and regressed separately. This research aims to show how distributed computing, particularly the divide and conquer approach implemented by Apache Spark, can be used to improve the efficiency and accuracy of LSMC in American option pricing. This paper provides an innovative solution to the financial market and could contribute to the advancement of American option pricing research.

Suggested Citation

  • Lu Xiong & Jiyao Luo & Hanna Vise & Madison White, 2023. "Distributed Least-Squares Monte Carlo for American Option Pricing," Risks, MDPI, vol. 11(8), pages 1-16, August.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:8:p:145-:d:1213150
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    References listed on IDEAS

    as
    1. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2018. "A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 6(2), pages 1-26, June.
    2. Edward M. H. Lin & Edward W. Sun & Min-Teh Yu, 2018. "Systemic risk, financial markets, and performance of financial institutions," Annals of Operations Research, Springer, vol. 262(2), pages 579-603, March.
    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. 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.
    5. 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.
    6. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    7. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2019. "Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension," Papers 1903.11275, arXiv.org, revised Dec 2019.
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