Short-Term Variations and Long-Term Dynamics in Commodity Prices

TLDR

Although these two factors are not directly observable, they may be estimated from spot and futures prices. In this article, we develop a two‑factor model of commodity prices that allows mean‑reversion in short‑term prices and uncertainty in the equilibrium level to which prices revert. The model is built on two factors—mean‑reverting short‑term price movements and stochastic equilibrium levels—using long‑maturity futures to infer the equilibrium and short‑term deviations, and its parameters are estimated from oil futures data. The model, though not explicitly modeling convenience yield dynamics, is equivalent to the Gibson–Schwartz stochastic convenience yield model, and its estimated parameters applied to oil‑linked assets demonstrate advantages over that model.

Abstract

In this article, we develop a two-factor model of commodity prices that allows meanreversion in short-term prices and uncertainty in the equilibrium level to which prices revert. Although these two factors are not directly observable, they may be estimated from spot and futures prices. Intuitively, movements in prices for long-maturity futures contracts provide information about the equilibrium price level, and differences between the prices for the short- and long-term contracts provide information about short-term variations in prices. We show that, although this model does not explicitly consider changes in convenience yields over time, this short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990). We estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil-linked assets to demonstrate its use and some of its advantages over the Gibson-Schwartz model.