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American Options on Dividend-Paying Assets

Author

Listed:
  • Mark Broadie
  • Jérôme Detemple

Abstract

We provide a comprehensive treatment of option pricing with particular emphasis on the valuation of American options on dividend-paying essets. We begin by reviewing valuation principles for European contingent claims in a financial market in which the underlying asset price follows an Itô process and the interest rate is stochastic. Then this anlysis is extended to the valuation of American contingent claims. In particular, the early exercise premium and the delayed exercise premium representations of the American option price are presented. These results are specialized in the case of the standard market model, i.e., when the underlying asset price follows a geometric Brownian motion process and the interest rate is constant. American capped options with constant and growing caps are then analyzed. Valuation formulas are first provided for capped options on dividend-paying assets in the context of the standard market model. Previously unpublished results are then presented for capped options on nodividend-paying assets when the underlying asset price follows an Itô process with stochastic volatility and the cap's growth rate is an adapted stochastic process. Nous présentons un traitement compréhensif de l'évaluation des options américaines sur des actifs qui payent des dividendes. Nous passons tout d'abord en revue les principes d'évaluation de titres contingents européens dans le cadre d'un marché financier dans lequel le prix des actifs sous-jacents suit des processus d'Itô et le taux d'intérêt est stochastique. L'analyse est ensuite généralisée à l'évaluation des titres contingents américains. Nous présentons, en particulier, les représentations de prime d'exercice prématuré et de prime d'exercice délayé, du prix de l'option américaine. Ces résultats sont spécialisés au cas du modèle de marché standard, c'est-à-dire lorsque le prix de l'actif sous-jacent suit un mouvement Brownien géométrique et le taux d'intérêt est constant. Les options américaines plafonnées, avec plafond constant ou croissant, sont ensuite analysées. Des formules d'évaluation sont tout d'abord présentées pour les options plafonnées sur des actifs à dividendes dans le contexte du modèle standard. Des résultats nouveaux sont ensuite présentés pour les options plafonnées sur des actifs sans dividende lorsque le prix du sous-jacent suit un processus d'Itô à volatilité stochastique et le taux de croissance du plafond est un processus stochastique adapté.

Suggested Citation

  • Mark Broadie & Jérôme Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO.
    • Handle: RePEc:cir:cirwor:96s-16
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    References listed on IDEAS

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