Equilibrium Forward Curves for Commodities

We develop an equilibrium model of the term structure of forward prices for commodities. Our approach differs from Brennan (1991) and Schwartz (1997) and other two-factor approaches in that we do not assume an exogenous "convenience yield" process as a second factor in forward prices. Rather, we view the spot commodity as having an embedded timing option that is absent in a forward contract. The value of this timing option arises from a non- negativity constraint on inventory. The value changes over time as a function of both the endogenous inventory level and exogenous shocks to supply and demand. In contrast to the two-factor models, our model exhibits a state dependent correlation between spot prices and convenience yields. We also use our model to understand the relation among the volatilities of forward prices at different horizons. We show how conditional violations of the Samuelson effect can occur. We also address the related issue of dynamically trading a near-dated forward contract to hedge a long- dated position. Finally, our model is adapted to incorporate seasonalities in commodity demand and production.