What do market-calibrated stochastic processes indicate about the long-term price of crude oil?

Abstract

Stochastic process models of commodity prices are important inputs in energy investment evaluation and planning problems. In this paper, we focus on modeling and forecasting the long-term price level, since it is the dominant factor in many such applications. To provide a foundation for our modeling approach we first evaluate the empirical characteristics of crude oil price data from 1990 to 2013 using unit root and variance ratio tests. Statistical evidence from these tests shows only weak support for the applicability of stationary mean-reverting type processes up through 2004, with non-stationary Brownian motion type processes becoming more plausible when the data from 2005 to 2013 is added. We then apply a Kalman filtering method with maximum likelihood approach to estimate the model parameters for both a single-factor Geometric Brownian motion (GBM) process as well as the two-factor Schwartz and Smith (2000) process. The latter process decomposes the spot price into unobservable factors for the long-term equilibrium level and short-term deviation, and it accommodates aspects of both a GBM process and a mean-reverting process. Both empirical and simulated data are analyzed with these models, and we quantify the increases in both the drift rate and volatility of these processes that result from developments in the crude oil markets since the middle of the last decade. We conclude by comparing and contrasting both historical accuracy and forecasts from the parameterized models, and show that when the emphasis is on the long-term expectations, a single factor GBM forecast may be sufficient.