Double barrier hitting time distributions with applications to exotic options

Abstract

In this paper we derive two defective density functions related to double barrier hitting probabilities of a geometric Brownian motion. A technique developed by Gerber and Shiu (1994, 1996) and Laplace transforms are used. Our approach is simple and straightforward, and purely analytical. We then apply the formulas to value some exotic options whose payoffs are contingent on barrier hitting time. This work is motivated by a recent development of equity indexed annuities in the United States.