Abstract
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.
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Chesney, M., Gauthier, L. American Parisian options. Finance Stoch 10, 475–506 (2006). https://doi.org/10.1007/s00780-006-0015-3
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DOI: https://doi.org/10.1007/s00780-006-0015-3