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

Philip Protter (), Emmanuelle Clément and Damien Lamberton
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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

Finance and Stochastics, 2002, vol. 6, issue 4, 449-471

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.

Keywords: American options; optimal stopping; Monte-Carlo methods; least squares regression (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: April 2001; final version received: January 2002
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Citations: View citations in EconPapers (100)

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