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Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates




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    • Jaime Casassus is from the Escuela de Ingeniería de la Pontificia Universidad Católica de Chile. Pierre Collin-Dufresne is from the University of California, Berkeley. Most of the work was completed while both authors were at Carnegie Mellon University. We thank Jesper Andreasen; Stephan Dieckmann; Bob Goldstein; Bryan Routledge; Eduardo Schwartz; Fallaw Sowell; Sanjay Srivastava, Stan Zin; seminar participants at UC Berkeley, Carnegie Mellon University, the University of Madison-Wisconsin, the University of Southern California, the 2002 European Finance Association, the 2004 Western Finance Association; an anonymous referee; and the editor, Suresh Sundaresan. Casassus acknowledges financial support from MIDEPLAN and FONDECYT (grant 1040328).


We characterize a three-factor model of commodity spot prices, convenience yields, and interest rates, which nests many existing specifications. The model allows convenience yields to depend on spot prices and interest rates. It also allows for time-varying risk premia. Both may induce mean reversion in spot prices, albeit with very different economic implications. Empirical results show strong evidence for spot-price level dependence in convenience yields for crude oil and copper, which implies mean reversion in prices under the risk-neutral measure. Silver, gold, and copper exhibit time variation in risk premia that implies mean reversion of prices under the physical measure.

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