Perpetual American Options and Real Options Under Mean-Reverting Processes

We calculate optimal exercise boundaries and rational prices for perpetual American call and put options, and solve entry and exit problems when the underlying uncertainty is modelled as an exponential Ornstein-Uhlenbeck process. The solution is almost as simple as in the case of an exponential (geometric) Brownian motion although the equations for the optimal exercise boundary are more involved. We show that in the real option framework, the difference between the option values in the Ornstein-Uhlenbeck model and corresponding Brownian motion model can be very large even when the difference between the thresholds is several percent only. For embedded options, the difference becomes especiallylarge