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The Valuation of American Options on Multiple Assets

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  • Mark Broadie
  • Jérôme B. Detemple

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    Abstract

    In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First we characterize the optimal exercises regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and option on the arithmetic average of two assets. Second, we also consider a class of contracts with nonconvex payoffs, such as American capped exchange options. For this option we explicitly identify the optimal exercise boundary and provide a decomposition of the price in terms of capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior to reaching the cap. Beside generalizing the current literature on American option valuation our analysis also has implications for the macroeconomic theory of investment under uncertainty. A specialization of one of our models also provides a new representation formula for an American capped option on a single underlying asset. Dans cet article nous établissons des formules d'évaluation pour un ensemble d'options américaines sur deux ou plus actifs sous-jacents. Notre contribution est de deux ordres. En premier lieu nous caractérisons la région d'exercice optimale et établissons des formules d'évaluation pour un nombre de contrats d'options américaines à actifs multiples sous-jacents et à fonctions de gains convexes. Des exemples incluent les options sur le maximum de deux actifs, les options à double prix d'exercice, les options sur différentiels, les options d'échange, les options sur le produit et les puissances du produit, et les options sur la moyenne arithmétique de deux actifs. En deuxième lieu, nous considérons également une classe de contrats à gains non-convexes tels que les options d'échange américaines avec plafond. Pour cette option nous identifions de manière explicite la frontière d'exercice optimale et nous établissons une décomposition en termes d'une option d'échange avec plafond avec exercice automatique lorsque le plafond est atteint et d'une prime d'exercice prématuré qui dépend des bénéfices réalisés lorsque l'exercice précède l'atteinte du plafond. Outre la généralisation de la littérature présente sur l'évaluation des options américaines, notre analyse a également des conséquences pour la théorie macro-économique de l'investissement dans l'incertain. Une spécialisation d'un de nos modèles constitue également une nouvelle formule de représentation pour une option américaine avec plafond sur un actif sous-jacent unique.

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    File URL: http://www.cirano.qc.ca/pdf/publication/94s-08.pdf
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    Bibliographic Info

    Paper provided by CIRANO in its series CIRANO Working Papers with number 94s-08.

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    Date of creation: 01 Sep 1994
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    Handle: RePEc:cir:cirwor:94s-08

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    Keywords: Option valuation; Underlying assets ; Capped exchange options; Évaluation d'options ; Actifs sous-jacents ; Options avec plafond;

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    Cited by:
    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.

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