Equilibrium Forward Curves for Commodities


  • Bryan R. Routledge,

  • Duane J. Seppi,

  • Chester S. Spatt

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    • Graduate School of Industrial Administration, Carnegie Mellon University. We thank René Stulz and an anonymous referee for their helpful advice and David Backus, Jonathan Berk, Frank de Jong, Eric Ghysels, Rick Green, Rob Heinkel, Glen Kentwell, John Lehoczky, Bart Lipman, Kristian Miltersen, R. (Nic) Nicolaides, Christine Parlour, Pedro Santa Clara, Eduardo Schwartz, Steven Shreve, Sridhar Tayur, and Harold Zhang for comments. We also thank seminar participants at Carnegie Mellon, Northwestern, Penn State, Toulouse, UC Berkeley, UCLA, the University of Iowa, the University of Texas at Austin, the University of Vienna, the Vienna Institute for Advanced Studies, and Yale as well as at the Seventh Annual Derivative Securities Conference at Queen's University, the 1997 NBER Summer Asset Pricing Workshop, the 1997 European Finance Association, the 1998 American Finance Association, and the 1998 Q-Group meetings. The Decision, Risk, and Management Science Program of the National Science Foundation and the Institute for Quantitative Research in Finance provided financial support for this research. The Q-Group also awarded the paper its 1998 Roger Murray Prize.


We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option's value changes over time due to both endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about volatilities of forward prices at different horizons and shows how conditional violations of the ‘Samuelson effect’ occur. We extend the model to incorporate a permanent second factor and calibrate the model to crude oil futures data.