Correcting the Bias in Monte Carlo Estimators of American-style Option Values

K. H. Felix Kan (), R. Mark Reesor (), Tyson Whitehead () and Matt Davison ()
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K. H. Felix Kan: The University of Western Ontario, Department of Applied Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 439-454 from Springer

Abstract: Abstract Existing Monte Carlo estimators of American option values are consistent but biased. This article presents a general bias reduction technique which corrects the bias due to making suboptimal exercise decisions. The derived asymptotic expression for the bias is independent of dimensionality, holds for very general underlying processes and option payoffs, and is easily evaluated. The bias is subtracted from the estimators at each exercise opportunity in order to produce bias-corrected estimators. We illustrate how to apply this technique to three methods of generating estimators — stochastic tree, stochastic mesh and least-squares Monte Carlo. Numerical results demonstrate that for a fixed sample size this technique significantly reduces the relative error for both high- and low-biased estimators.

Keywords: Monte Carlo; American Option; Average Relative Error; Option Payoff; Exercise Boundary (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_28

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DOI: 10.1007/978-3-642-04107-5_28

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