A Discrete-Time Approach for Valuing Real Options with Underlying Mean-Reverting Stochastic Processes

Acknowledgements I wish to thank my dissertation advisor, Professor James S. Dyer for his insights and guidance. I would also like to recognize the other members of my dissertation Their comments and service were greatly appreciated. Dr. Luiz Brandao also provided many useful insights, and Dr. Jim Smith and Dr. John Butler were very helpful with computational matters. I would like to thank my parents, Warren and Katie Hahn for their constant encouragement and for all the sacrifices they made over the years to support my education. I am also particularly indebted to my godparents, J.T. and Carolyn Smith for their support and guidance, and to my grandmother Willodene Watkins Smith for impressing upon me at a very early age the importance of educational opportunity. Finally, I want to express my deep appreciation to my wife Lori and daughters Allison and Lindsey for their love, encouragement, patience and understanding during both the MBA and Ph.D. programs. In this research the recombining binomial lattice approach for valuing real options is generalized to address a common issue in many real valuation problems, underlying stochastic processes that are mean-reverting. Binomial lattices were first introduced to approximate stochastic processes for valuation of financial options, and they provide a convenient framework for numerical analysis. Unfortunately, the standard approach to constructing binomial lattices can result in invalid probabilities of up and down moves in the lattice when a mean-reverting stochastic process is to be approximated. There have been several alternative methods introduced for modeling mean-reverting processes, including simulation-based approaches and trinomial trees, however they unfortunately complicate the numerical analysis of valuation problems. The approach developed in this research utilizes a more general binomial approximation methodology from the existing literature to model simple homoskedastic mean-reverting stochastic processes as recombining lattices. This approach is then extended to model a two-factor mean-vii reverting process that allows for uncertainty in the long-term mean, and to model two correlated one-factor mean-reverting processes. These models facilitate the evaluation of real options with early-exercise characteristics, as well as multiple concurrent options. The models developed in this research are tested by implementing the lattice in binomial decision tree format and applying to hypothetical real option examples with underlying mean-reverting commodity price. To specify the stochastic process for commodity price, different data analysis techniques such as Kalman filtering and seemingly unrelated regression are used. These different techniques are empirically tested to evaluate differences in the …