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A critical analysis of the Weighted Least Squares Monte Carlo method for pricing American options

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  • Reesor, R. Mark
  • Stentoft, Lars
  • Zhu, Xiaotian

Abstract

Least-squares Monte Carlo generates regression-based continuation value estimators that are heteroscedastic. Fabozzi et al. (2017) propose weighted least-squares regression to correct for this. We show that heteroscedastic-corrected estimators are more accurate than uncorrected estimators far from the exercise boundary and where the exercise decision is obvious. However, the corrected estimators do not translate into improved exercise decisions and hence correcting has little effect on option price estimates. This holds when using alternative specifications for the correction and when implementing an iterative method. We conclude that correcting for heteroscedasticity does not result in more efficient prices and generally should be avoided.

Suggested Citation

  • Reesor, R. Mark & Stentoft, Lars & Zhu, Xiaotian, 2024. "A critical analysis of the Weighted Least Squares Monte Carlo method for pricing American options," Finance Research Letters, Elsevier, vol. 64(C).
    • Handle: RePEc:eee:finlet:v:64:y:2024:i:c:s1544612324004094
    DOI: 10.1016/j.frl.2024.105379
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    References listed on IDEAS

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    1. 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.
    2. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    3. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-889, July.
    4. 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.
    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. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    7. 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.
    8. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    9. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.
    10. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    11. Brennan, Michael J. & Schwartz, Eduardo S., 1977. "Abstract: Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 659-659, November.
    12. Kin Hung (Felix) Kan & R. Mark Reesor, 2012. "Bias Reduction for Pricing American Options by Least-Squares Monte Carlo," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 195-217, July.
    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.
    14. Fabozzi, Frank J. & Paletta, Tommaso & Tunaru, Radu, 2017. "An improved least squares Monte Carlo valuation method based on heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 263(2), pages 698-706.
    15. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, August.
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    More about this item

    Keywords

    American options; Heteroscedasticity corrections; Regression; Simulation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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