Modelling Real Options: A First Passage Time Approach

This paper introduces the first passage time approach to study optimal option exercise rule for geometric Brownian motion process to a boundary. I have derived analytical results on the first passage time probability, density and its expectation. The results on the first moment of the first passage time clarify some recent controversies on the sign of uncertainty on investment. The first passage time provides an alternative characterisation of optimal exercise rule. In addition, we establish a new framework for testing real option models. The approach is applicable to other stochastic modelling in finance and economics.