AN ANALYTICAL SOLUTION FOR THE TWO‐SIDED PARISIAN STOPPING TIME, ITS ASYMPTOTICS, AND THE PRICING OF PARISIAN OPTIONS. (16th June 2015)

• Record Type: Journal Article
• Authors: Dassios, Angelos; Lim, Jia Wei
• Is Part Of: Mathematical finance. Volume 27:Number 2(2017:Apr.)
• Page Start: 604
• Page End: 620
• Publication Date: 2015-06-16
• Subjects: Brownian excursion -- double‐sided Parisian options -- tail asymptotics; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12091
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract : In this paper, we obtain a recursive formula for the density of the two‐sided Parisian stopping time. This formula does not require any numerical inversion of Laplace transforms, and is similar to the formula obtained for the one‐sided Parisian stopping time derived in Dassios and Lim. However, when we study the tails of the two distributions, we find that the two‐sided stopping time has an exponential tail, while the one‐sided stopping time has a heavier tail. We derive an asymptotic result for the tail of the two‐sided stopping time distribution and propose an alternative method of approximating the price of the two‐sided Parisian option.