Equilibrium Former Curves for Commodities
Bryan R. Routledge, Carnegie Mellon University
Duane J. Seppi, Carnegie Mellon University
Chester S. Spatt, Carnegie Mellon University

This paper presents an equilibrium model of the term structure of forward prices for storable commodities. Our approach differs from Brennan (1991) and Schwartz (1997) in that we do not explicitly assume an exogenous “convenience yield.” Rather, our spot commodity has an embedded timing option that is absent in forward contracts, which arises from a non-negativity constraint on inventory. The value of this option changes over time as a function of both the endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about the volatilities of forward prices at different horizons and shows how conditional violations of the “Samuelson effect” can occur. We address the related issue of dynamically trading near-dated forward contracts to hedge a long-dated position. We also present a tractable extension of the model with a permanent second factor and a calibration of the model to crude oil futures price data. (Accepted Late Spring 1999.)