A Dynamic Programming Procedure for Pricing American-Style Asian Options

Hatem Ben-Ameur (), Michèle Breton () and Pierre L'Ecuyer ()
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Hatem Ben-Ameur: GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7
Michèle Breton: GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7
Pierre L'Ecuyer: GERAD and Département d'Informatique et de Recherche Opérationnelle Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Canada H3C 3J7 http://www.iro.umontreal.ca/~lecuyer

Management Science, 2002, vol. 48, issue 5, 625-643

Abstract: Pricing European-style Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no easily computable analytical solution is available. Pricing their American-style counterparts, which provide early exercise opportunities, poses the additional difficulty of solving a dynamic optimization problem to determine the optimal exercise strategy. A procedure for pricing American-style Asian options of the Bermudan flavor, based on dynamic programming combined with finite-element piecewise-polynomial approximation of the value function, is developed here. A convergence proof is provided. Numerical experiments illustrate the consistency and efficiency of the PROCEDURE. Theoretical properties of the value function and of the optimal exercise strategy are also established.

Keywords: Option Pricing; Asian Options; Path-Dependent Options; American Options; Bermudan Options; Dynamic Programming; Piecewise Polynomials (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (15)

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