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Primary Article

Enhancing the Accuracy of Pricing American and Bermudan Options

Peter W. Duck, David P. Newton, Martin Widdicks and Yan Leung
The Journal of Derivatives Summer 2005, 12 (4) 34-44; DOI: https://doi.org/10.3905/jod.2005.517184
Peter W. Duck
A professor of mathematics at the University of Manchester in Manchester,UK.
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  • For correspondence: duck@ma.man.ac.uk
David P. Newton
A professor of finance at Nottingham University Business School in Nottingham,UK.
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  • For correspondence: david.newton@nottingham.ac.uk
Martin Widdicks
A senior lecturer at Manchester Business School in Manchester.
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  • For correspondence: m.widdicks@mbs.ac.uk
Yan Leung
A graduate student in mathematics at the University of Manchester.
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  • For correspondence: yleung@maths.man.ac.uk
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Abstract

A technique recently developed by Longstaff and Schwartz (LS) significantly enhances the Monte Carlo technology for pricing American options, by using regression to streamline the analysis of the subsidiary future paths in modeling the early exercise decisions. But the procedure still requires a large amount of computation and the degree of difficulty explodes as the number of stochastic factors in the problem increases. In this article, the authors show several alterations to the LS approach that can increase its efficiency substantially. The most important involves setting up the problem as a kind of Monte Carlo analysis of Monte Carlo models. For each run, they construct three estimates of the option value using different numbers of simulated paths, for example 1,000, 2,000, and 4,000 paths. This process is then repeated for many runs. Averaging across these multiple Monte Carlo estimates produces a set of three average values that are then used in an extrapolation procedure to estimate the option value that would be produced with an infinite number of paths. The improvement in performance from this two-part strategy is striking, as the authors demonstrate by pricing a Bermudan put option on five underlyings.

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The Journal of Derivatives
Vol. 12, Issue 4
Summer 2005
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Enhancing the Accuracy of Pricing American and Bermudan Options
Peter W. Duck, David P. Newton, Martin Widdicks, Yan Leung
The Journal of Derivatives May 2005, 12 (4) 34-44; DOI: 10.3905/jod.2005.517184

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Enhancing the Accuracy of Pricing American and Bermudan Options
Peter W. Duck, David P. Newton, Martin Widdicks, Yan Leung
The Journal of Derivatives May 2005, 12 (4) 34-44; DOI: 10.3905/jod.2005.517184
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