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

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  • 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," JRFM, MDPI, 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

    as
    1. 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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    Cited by:

    1. Lars Stentoft, 2020. "Computational Finance," JRFM, MDPI, vol. 13(7), pages 1-4, July.
    2. Chinonso Nwankwo & Nneka Umeorah & Tony Ware & Weizhong Dai, 2022. "Deep learning and American options via free boundary framework," Papers 2211.11803, arXiv.org, revised Dec 2022.

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