Discrete time modeling of mean-reverting stochastic processes for real option valuation

Abstract

In this paper the recombining binomial lattice approach for modeling real options and valuing managerial flexibility is generalized to address a common issue in many practical applications, 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 paper 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 dual correlated one-factor mean-reverting processes. These models facilitate the evaluation of options with early-exercise characteristics, as well as multiple concurrent options. The models we develop in this paper are tested by implementing the lattice in binomial decision tree format and applying to a real application by solving for the value of an oil and gas switching option which requires a binomial model of two correlated one-factor commodity price models. For cases where the number of discrete time periods becomes too large to be solved using common decision tree software, we describe how recursive dynamic programming algorithms can be developed to generate solutions.