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American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods

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  • Mark Broadie
  • Jérôme B. Detemple

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    Abstract

    In this paper we provide lower and upper bounds on the prices of American call and put options written on a dividend paying asset. Based on the bounds, we provide two option price approximations. Our second approximation, which uses both lower and upper bound information, has an average accuracy comparable to a 1000-step binomial tree with a computation speed comparable to a 50-step binomial tree. Put another way, our second approximation is 6 times more accurate than a 200-step binomial tree and is about 15 times faster than a 200-step binomial tree. Furthermore, the approximations are sufficiently simple that they can be computed in a spreadsheet. In addition, we conduct a careful large-scale evaluation of many recent methods for computing American option prices. Comparisons are made on the basis of accuracy and speed of computation and lead to some surprising results. Dans cet article nous proposons des bornes inférieures et supérieures sur les prix d'options américaines à l'achat et à la vente. Sur la base de ces bornes nous proposons deux approximations du prix de l'option. Notre deuxième approximation qui utilise à la fois l'information sur la borne inférieure et supérieure a une précision moyenne comparable à un arbre binomial de 1000 pas avec une vitesse de calcul comparable à un arbre binomial de 50 pas. En d'autre termes notre deuxième approximation est 6 fois plus précise qu'un arbre binomial à 200 pas et est 15 fois plus rapide qu'un arbre binomial à 200 pas. De plus les approximations sont suffisamment simple pour être calculées dans un tableur (spreadsheet). En outre, nous effectuons une évaluation soigneuse et sur grande échelle des nombreuses méthodes numériques qui ont été proposées récemment pour calculer les prix des options américaines. Ces comparaisons sont faites sur la base de la précision et de la vitesse de calcul et conduisent à certains résultats surprenant.

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    File URL: http://www.cirano.qc.ca/pdf/publication/94s-07.pdf
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    Bibliographic Info

    Paper provided by CIRANO in its series CIRANO Working Papers with number 94s-07.

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    Date of creation: 01 Sep 1994
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    Handle: RePEc:cir:cirwor:94s-07

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    Related research

    Keywords: Option price approximations; Approximations du prix de l'option;

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    Cited by:
    1. Leisen, D. P. J. & M. Reimer, 1995. "Binomial Models for Option Valuation - Examining and Improving Convergence," Discussion Paper Serie B 309, University of Bonn, Germany.

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