An analytical solution for the two-sided Parisian stopping time, its asymptotics and the pricing of Parisian options

Angelos Dassios and Jia Wei Lim

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 [6]. 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 stop- ping 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.

Keywords: Brownian excursion; double-sided Parisian options; tail asymptotics (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2017-04-01
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Citations: View citations in EconPapers (3)

Published in Mathematical Finance, 1, April, 2017, 27(2), pp. 604-620. ISSN: 0960-1627

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