Hedging entry and exit decisions: Activating and deactivating barrier options (Q1613226)

This paper introduces and prices a new type of options in the context of deciding whether to enter or exit from an investment project. These switch options are similar to barrier options in that they are activated or deactivated when their underlying hits a barrier, but the number of changes between active and inactive is not limited to only one. For the case where the traded underlying is a geometric Brownian motion, the paper obtains an explicit formula for the value of a switch option by deriving the joint law of the Brownian meander and its running supremum. The paper also explains how such options can be used for hedging risks related to sub-optimal entry or exit decisions.