The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging



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    • Anderson Graduate School of Management, University of California Los Angeles. This article was prepared for the Presidential Address of the American Finance Association meetings in New Orleans, January 1997. I thank Richard Roll, Alan Kraus, Ernest Greenwood, and Kristian Miltersen for suggestions and Olivier Ledoit, Piet de Jong and Julian Franks for helpful discussions. I especially thank Michael Brennan, not only for his comments on this article, but for 25 years of inspiration, advice, and friendship. Part of this research was done while I was a visiting scholar at the University of British Columbia during the summer of 1996.


In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions.