Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motion

We investigate a class of optimal stopping problems arising in, forexample, studies considering the timing of an irreversible investment whenthe underlying follows a skew Brownian motion. Our results indicate that thelocal directional predictability modeled by the presence of a skew point forthe underlying has a nontrivial and somewhat surprising impact on the timingincentives of the decision maker. We prove that waiting is always optimal atthe skew point for a large class of exercise payoffs. An interesting consequenceof this finding, which is in sharp contrast with studies relying on ordinaryBrownian motion, is that the exercise region for the problem can becomeunconnected even when the payoff is linear. We also establish that higherskewness increases the incentives to wait and postpones the optimal timing ofan investment opportunity. Our general results are explicitly illustrated for apiecewise linear payoff.