Real Option Pricing with Mean-Reverting Investment and Project Value (Extended Version)
Jorge Zubelli | Jaimungal, Sebastian | Souza, Max
Mean-Reverting; Stochastic Investment; Investment under Uncertainty
n 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, mean-reverting 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.