Description:
In this work we are concerned with valuing the option to invest in a project when the project value and the investment value are both mean-reverting. Previous works which dealt with stochastic project and investment value concentrate on geometric Brownian motions for driving the values. However, when the project involved is linked to commodities, meanreverting assumptions are more meaningful. Here, we introduce a model and prove that the optimal exercise strategy is not a function of ratio of project value to investment V=I { as it is in the Brownian case. We further apply the Fourier space time-stepping algorithm of Jaimungal and Surkov (2009) to numerically investigate the option to invest. The optimal exercise policies are found to be approximately linear in V=I; however, the intercept is not zero.