Modern asset pricing methods that account for managerial flexibility in project valuation require the specification of the stochastic processes followed by commodity prices and by other underlying uncertainties. Simplifying assumptions about these processes can be made to facilitate numerical analysis using binomial trees or lattices; however these assumptions are often untenable. An example is the assumption of a stochastic process for commodity price that is lognormally distributed with variance that grows linearly with time, commonly referred to as a Geometric Brownian Motion (GBM). Although GBM processes are convenient for modeling, they produce forecasts that do not match the empirical evidence of mean-reversion in commodity prices, and result in significant errors in valuation. Several methods have been introduced for modeling mean-reversion, but they complicate the numerical analysis of valuation problems.
In this paper we discuss a new method for modeling mean-reverting processes that enables straightforward binomial tree and lattice-based approaches to valuation. We provide an illustration by applying this method to model a one-factor mean-reverting price process, and then use this model in the valuation of an example oil and gas project with downstream managerial flexibility. We also solve the example using an alternative method, monte carlo simulation, and show that our results are identical to those obtained from this more computationally intensive approach.