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Bias Reduction for Pricing American Options by Least-Squares Monte Carlo

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  • Kin Hung (Felix) Kan
  • R. Mark Reesor

Abstract

We derive an approximation to the bias in regression-based Monte Carlo estimators of American option values. This derivation holds for general asset-price processes of any dimensionality and for general pay-off structures. It uses the large sample properties of least-squares regression estimators. Bias-corrected estimators result by subtracting the bias approximation from the uncorrected estimator at each exercise opportunity. Numerical results show that the bias-corrected estimator outperforms its uncorrected counterpart across all combinations of number of exercise opportunities, option moneyness and sample size. Finally, the results suggest significant computational efficiency increases can be realized through trivial parallel implementations using the corrected estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:195-217
    DOI: 10.1080/1350486X.2011.608566
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    Cited by:

    1. 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).
    2. Michael Ludkovski, 2015. "Kriging Metamodels and Experimental Design for Bermudan Option Pricing," Papers 1509.02179, arXiv.org, revised Oct 2016.
    3. Mark S. Joshi, 2016. "Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 519-533, April.
    4. Francesco Rotondi, 2019. "American Options on High Dividend Securities: A Numerical Investigation," Risks, MDPI, vol. 7(2), pages 1-20, May.

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