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

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
  • 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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    More about this item

    Keywords

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

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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