Real Option Pricing with Mean-Reverting Investment and Project Value
Jaimungal, Sebastian, Max O. De Souza, and Jorge P. Zubelli. "Real option pricing with mean-reverting investment and project value." The European Journal of Finance 19.7-8 (2013): 625-644.
28 Pages Posted: 17 Oct 2010 Last revised: 27 Apr 2015
Date Written: October 17, 2010
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.
Keywords: Real Options, Mean-Reverting, Investment under Uncertainty, Uncertain Costs
JEL Classification: C6, C61, C67
Suggested Citation: Suggested Citation