Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder <italic>et al.</italic> [<italic>J</italic>. <italic>Finance</italic>, 1995, <bold>50</bold>, 361--375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson--Schwartz [<italic>J</italic>. <italic>Finance</italic>, 1990, <bold>45</bold>, 959--976] model and the Casassus--Collin-Dufresne [<italic>J</italic>. <italic>Finance</italic>, 2005, <bold>60</bold>, 2283--2331] model with a constant interest rate. An application for option pricing is also presented in this paper.