Real Option Pricing with Mean-Reverting Investment and Project Value

In this work we are concerned with valuing the option to invest in a project when the project value and the investment cost are both mean-reverting. Previous works on stochastic project and investment cost concentrate on geometric Brownian motions (GBMs) for driving the factors. However, when the project involved is linked to commodities, mean-reverting assumptions are more meaningful. Here, we introduce a model and prove that the optimal exercise strategy is not a function of the ratio of the project value to the investment V/I -- contrary to the GBM case. We also demonstrate that the limiting trigger curve as maturity approaches traces out a non-linear curve in the (V,I) plan and derive its explicit form. Finally, we numerically investigate the finite-horizon problem using the Fourier space time-stepping algorithm of Jaimungal & Surkov (2009). Numerically, the optimal exercise policies are found to be approximately linear in V/I; however, contrary to the GBM case they are not described by a curve of the form V^*/I^* = c(t). The option price behavior as well as the trigger curve behavior nicely generalize earlier one-factor model results