infonet-economy

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