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

See all articles by Sebastian Jaimungal

Sebastian Jaimungal

University of Toronto - Department of Statistics

Max O. Souza

Universidade Federal Fluminense - Instituto de Matemática e Estatística

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA)

Date Written: October 17, 2010

Abstract

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

Jaimungal, Sebastian and Souza, Max and Zubelli, Jorge P., Real Option Pricing with Mean-Reverting Investment and Project Value (October 17, 2010). 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., Available at SSRN: https://ssrn.com/abstract=1693562

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Max Souza

Universidade Federal Fluminense - Instituto de Matemática e Estatística ( email )

Rua Prof. Marcos Waldemar de Freitas Reis, S/N
Blocos G e H, Campus do Gragoatá,
Niterói, Rio de Janeiro 24210-201
Brazil

HOME PAGE: http://www.professores.uff.br/msouza

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA) ( email )

Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro, 22460
Brazil

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