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Nonparametric Estimation of American Options Exercise Boundaries and Call Prices

  • Mark Broadie
  • Jérôme B. Detemple
  • Eric Ghysels
  • Olivier Torrès

Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. The paper focuses on the daily market option prices and exercise data on the S&P100 contract. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries. Contrairement à ce qu'il est possible d'obtenir dans un contexte d'évaluation de titres dérivés de type européen, il n'existe pas de formule analytique simple pour évaluer les options américaines, même si la volatilité de l'actif sous-jacent est supposée constante. La possibilité d'exercice prématuré qu'offre ce type de contrat complique considérablement son évaluation. La démarche adoptée dans cette étude consiste à dériver les prix d'option et les frontières d'exercice à partir de données financières, utilisées dans un cadre d'analyse statistique non-paramétrique. Plus particulièrement, l'étude utilise les observations quotidiennes du prix du contrat sur l'indice S&P100 ainsi que les observations sur l'exercice de ce contrat. Les résultats sont comparés à ceux obtenus à l'aide de techniques paramétriques dans un modèle où la volatilité est supposée constante. La conclusion est qu'il existe des différences stratégiques entre les prédictions des deux modèles, aussi bien en ce qui concerne le prix de l'option que la politique d'exercice qui lui est associée.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 96s-24.

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Length: 38 pages
Date of creation: 01 Sep 1996
Date of revision:
Handle: RePEc:cir:cirwor:96s-24
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