Modeling Energy Commodity Futures

Abstract

The article analyzes the price dynamics of two important commodity futures prices? crude oil and natural gas. Some of the latest models of commodity prices are subjected to empirical testing here? specifically the two-factor model of Schwartz-Smith [2000], which nests other important models developed earlier. The two-factor model includes a mean-reverting short-term deviation and uncertain equilibrium level to which prices gravitate. The two factors are not directly observable but can be estimated from futures prices. This is the base case model in this study. The model parameters of the Schwartz-Smith two-factor model are estimated out of traded futures on natural gas and crude oil, using the fixed maturity format the author creates for futures prices. Analysis of the variance structure of natural gas prices suggests the presence of seasonality. Seasonal adjustment is performed and the model is estimated on the deseasonalized data. The effect of seasonality is studied using both the fixed-maturity price series and the original price series for all the models dealing with seasonality to judge whether the model implications and parameters change across the data series. The seasonally adjusted series produce a better fit to the two-factor model, as indicated by various goodness-of-fit metrics computed. Model-based seasonality approaches are developed as well, among which seasonal dummies and a three-factor model with a stochastic seasonality component of log spot prices. The modeled-in seasonality specifications explain futures prices for natural gas better than the base case of the two-factor model, with the three-factor model producing an especially good description of the prices at a certain point of time, but predicting log prices up to three years out in the future with larger errors than alternative models. The author runs a race between the various parameterized and non-parameterized versions of models with seasonality to test both their in-sample and out-of-sample prediction ability, gauged by the pricing errors they generate. The volatility functions model, based on principal components extraction from daily data, with seasonality in short-term volatility, seems to have the best forecasting ability, followed by the two-factor model on Kendall-type deseasonalized data and the seasonal dummies specification. The Bayesian information criterion (BIC) applied to all the parameterized models singles out the three-factor model, followed by the two-factor model on Kendall-type deseasonalized data of fixed maturity. The three-factor model, however, produces less accurate parameter estimates and larger prediction errors than the other models.