Real option pricing with mean-reverting investment and project value

Sebastian Jaimungal, Max O. de Souza, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 nonlinear curve in (V, I) space and derive its explicit form. Finally, we numerically investigate the finite-horizon problem, using the Fourier space time-stepping algorithm of Jaimungal and Surkov [2009. Lev́y based cross-commodity models and derivative valuation. SIAM Journal of Financial Mathematics, to appear.]. 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.

Original languageBritish English
Pages (from-to)625-644
Number of pages20
JournalEuropean Journal of Finance
Issue number7-8
StatePublished - Sep 2013


  • investment under uncertainty
  • mean-reverting
  • real options
  • stochastic investment


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