Damien Lamberton

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

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.

Critical Price for an American Option near Maturity

We give an alternate proof of a recent result of Barles, Burdeau, Romano and Samsoen on the behavior of the critical price for American put options near maturity.

RECURSIVE COMPUTATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION: THE CASE OF A WEAKLY MEAN REVERTING DRIFT

Laboratoire dAnalyse et de Mathematiques Appliquees, UMR 8050, Universite de Marne-laVallee, Cite Descartes, 5 boulevard Descartes, Champs-sur-Marne, F-77454 Marne-la-Vallee Cedex 2, France. E-mail: dlamb@math.univ-mlv.fr 2Laboratoire de Probabilites et Modcles Aleatoires, UMR 7599, Universite Pierre et Marie Curie, case 188, 4 place Jussieu, F-75252 Paris Cedex 05, France. E-mail: gpa@ccr.jussieu.fr