IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v12y2019i4p190-d298216.html
   My bibliography  Save this article

Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method

Author

Listed:
  • Pascal Létourneau

    () (Department of Finance and Business Law, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA)

  • Lars Stentoft

    () (Department of Economics and Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5C2, Canada)

Abstract

This paper proposes an innovative algorithm that significantly improves on the approximation of the optimal early exercise boundary obtained with simulation based methods for American option pricing. The method works by exploiting and leveraging the information in multiple cross-sectional regressions to the fullest by averaging the individually obtained estimates at each early exercise step, starting from just before maturity, in the backwards induction algorithm. With this method, less errors are accumulated, and as a result of this, the price estimate is essentially unbiased even for long maturity options. Numerical results demonstrate the improvements from our method and show that these are robust to the choice of simulation setup, the characteristics of the option, and the dimensionality of the problem. Finally, because our method naturally disassociates the estimation of the optimal early exercise boundary from the pricing of the option, significant efficiency gains can be obtained by using less simulated paths and repetitions to estimate the optimal early exercise boundary than with the regular method.

Suggested Citation

  • Pascal Létourneau & Lars Stentoft, 2019. "Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(4), pages 1-21, December.
  • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:4:p:190-:d:298216
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/12/4/190/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1911-8074/12/4/190/
    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," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, vol. 55(11), pages 1877-1896, November.
    3. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    4. repec:dau:papers:123456789/4273 is not listed on IDEAS
    5. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
    6. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    7. 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.
    8. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    9. Kang, Sang Baum & Létourneau, Pascal, 2016. "Investors’ reaction to the government credibility problem: A real option analysis of emission permit policy risk," Energy Economics, Elsevier, vol. 54(C), pages 96-107.
    10. Pascal L�tourneau & Lars Stentoft, 2014. "Refining the least squares Monte Carlo method by imposing structure," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 495-507, March.
    11. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    12. Denis Belomestny, 2011. "Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates," Finance and Stochastics, Springer, vol. 15(4), pages 655-683, December.
    13. 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. Lars Stentoft, 2020. "Computational Finance," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 13(7), pages 1-4, July.

    More about this item

    Keywords

    American options; least-squares Monte Carlo; exercise boundary; simulation;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics

    Statistics

    Access and download statistics

    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:gam:jjrfmx:v:12:y:2019:i:4:p:190-:d:298216. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (XML Conversion Team). General contact details of provider: https://www.mdpi.com/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.