Term Structure Models of Commodity Prices: A Review

This review article describes the main contributions in the literature on term structure models of commodity prices. The first section is devoted to the theoretical analysis of the term structure. It confines itself primarily to the traditional theories of commodity prices and to their explanation of the relationship between spot and futures prices. The theories of normal backwardation and storage are however a bit limited when the whole term structure is taken into account. As a result, there is a need for a long-term extension of the analysis, and this premise constitutes the second point of the section. Finally, a dynamic analysis of the term structure is presented. The second section is centered on term structure models of commodity prices. The presentation shows that these models differ on the nature and the number of factors used to describe uncertainty. Four different factors are generally used: the spot price, the convenience yield, the interest rate, and the long-term price. The third section reviews the main empirical results obtained with term structure models. First of all, simulations highlight the influence of the assumptions concerning the stochastic process retained for the state variables and the number of state variables. Then, the method usually employed for the estimation of the parameters is explained. Lastly, the models' performances, i.e., their ability to reproduce the term structure of commodity prices, are presented. The fourth section examines the two main applications of term structure models: hedging and valuation. The conclusion summarizes the broad trends in the literature on commodity pricing during the 1990s and early 2000s, and proposes future directions for research.