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American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation

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  • Mark Broadie
  • Jérôme B. Detemple

    ()

  • Eric Ghysels

    ()

  • Olivier Torrès

Abstract

In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility. Cet article examine les contrats optionnels de type américain lorsque l'actif sous-jacent paie des dividendes et a une volatilité stochastiques. Nous présentons une discussion complète des fondations théoriques de l'évaluation des options américaines et de leurs frontières d'exercice. Nous démontrons leur dépendance par rapport aux diverses sources d'incertitude qui déterminent le taux de dividendes et la volatilité, et dérivons les prix d'équilibre des actifs, titres dérivés ainsi que les politiques optimales d'exercice dans un modèle d'équilibre général. Les modèles théoriques conduisent à des expressions complexes qui sont difficiles à estimer. C'est pourquoi nous adoptons une approche non-paramétrique qui permet d'examiner des formes réduites. Nous utilisons des méthodes non-paramétriques pour estimer les prix d'options à l'achat et les frontières d'exercice conditionnelles aux dividendes et à la volatilité. Puisque cette dernière est un processus latent nous proposons plusieurs approches, fondées en particulier sur des estimateurs-filtres EGARCH, des volatilités implicites et historiques. L'approche non-paramétrique nous permet de tester si les prix d'options et les décisions d'exercice sont principalement déterminés par les dividendes, comme suggéré par Harvey et Whaley (1992a, b) et Fleming et Whaley (1994) pour le contrat OEX, ou si la volatilité stochastique complémente l'incertitude sur les dividendes. Nous établissons que les dividendes seuls ne rendent pas compte de tous les aspects de l'évaluation de ces options et des décisions d'exercice, ce qui suggère la nécessité d'inclure la volatilité stochastique.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 96s-26.

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Date of creation: 01 Oct 1996
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Handle: RePEc:cir:cirwor:96s-26

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Keywords: Option Pricing; Derivative Securities; OEX Contract; Kernel Estimation; Prix d'options; titres dérivés; contrat OEX; estimation par méthode de noyau;

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