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An analysis of a least squares regression method for American option pricing

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Author Info

  • Philip Protter

    ()
    (Operations Research and Industrial Engineering Department, Cornell University, Ithaca, NY 14853-3801, USA Manuscript)

  • Emmanuelle Clément

    (Équipe d'Analyse et de mathématiques appliquées, Université de Marne-la-Vallée, 5 Bld Descartes, Champs-sur-marne, 77454 Marne-la-Vallée Cedex 2, France)

  • Damien Lamberton

    (Équipe d'Analyse et de mathématiques appliquées, Université de Marne-la-Vallée, 5 Bld Descartes, Champs-sur-marne, 77454 Marne-la-Vallée Cedex 2, France)

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    Abstract

    Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. Under fairly general conditions, we prove the almost sure convergence of the complete algorithm. We also determine the rate of convergence of approximation two and prove that its normalized error is asymptotically Gaussian.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 4 ()
    Pages: 449-471

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:449-471

    Note: received: April 2001; final version received: January 2002
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: American options; optimal stopping; Monte-Carlo methods; least squares regression;

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