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American Parisian options

Chesney, Marc ; Gauthier, Laurent

In: Finance and Stochastics, 2006, vol. 10, no. 4, p. 475-506

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    Titre
    • American Parisian options
    Auteur
    • Chesney, Marc. University of Zurich, ISB, Plattenstrasse 14, 8032, Zurich, Switzerland
    • Gauthier, Laurent. 54 Greene Str., 10013, New York, NY, USA
    Type de document
    • Postprint
    Identifiant OAI-PMH
    • oai:doc.rero.ch:317462
    Summary
    In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non-perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the perpetual case, closed-form solutions or approximations are obtained by relying on excursion theory. We derive the Laplace transform of the first instant Brownian motion reaches a positive level or, without interruption, spends a given amount of time below zero. We perform a detailed comparison of perpetual standard, barrier and Parisian options