Double Barrier Hitting Time Distribution of a Mean-Reverting Lognormal Process and its Application to Pricing Exotic Options

Abstract

In this paper we propose a simple and easy-to-use method for computing accurate estimate (in closed form) of the double barrier hitting time distribution of a mean-reverting lognormal process, and discuss its application to pricing exotic options whose payoffs are contingent upon barrier hitting times. This new approach is also able to provide tight upper and lower bounds (in closed form) of the exact result. Within the multi-stage approximation scheme, the estimate and bounds can be easily improved in a systematic manner. Furthermore, this approach can be straight-forwardly extended to those cases with specified moving boundaries as well.