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


  • 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)


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

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    References listed on IDEAS

    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.
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    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.
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    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.
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    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.
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    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


    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


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