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.

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.

Eduardo S. Schwartz, The Pricing of Commodity-Linked Bonds, The Journal of Finance, Vol. 37, No. 2, Papers and Proceedings of the Fortieth Annual Meeting of the American Finance Association, Washington, D.C., December 28-30, 1981 (May, 1982), pp. 525-539

Eduardo S. Schwartz, Who Should Buy Portfolio Insurance?: Discussion, The Journal of Finance, Vol. 35, No. 2, Papers and Proceedings Thirty-Eighth Annual Meeting American Finance Association, Atlanta, Georgia, December 28-30, 1979 (May, 1980), pp. 595-596

Eduardo S. Schwartz, Theories of Corporate Debt Policy: A Synthesis: Discussion, The Journal of Finance, Vol. 34, No. 2, Papers and Proceedings, Thirty-Seventh Annual Meeting, American Finance Association, Chicago, Illinois, August 29-31, 1978 (May, 1979), pp. 386-387

Patricia J. Hughes, Eduardo S. Schwartz, The LIFO/FIFO Choice: An Asymmetric Information Approach, Journal of Accounting Research, Vol. 26, Studies on Management's Ability and Incentives to Affect the Timing and Magnitude of Accounting Accruals (1988), pp. 41-58

We examine the lead–lag relation between intraday spot and futures prices for a stock index where the component stocks are floor traded while the futures contract is screen traded. We find that futures prices lead spot prices by nearly 20 min. This is much longer than in markets where both the index and index futures are floor traded. We show that this lead–lag relation is unlikely to be an artifact of differences in liquidity between the spot and futures markets. These results are consistent with the hypothesis that screen trading accelerates the price discovery process. Journal of Economic Literature Classification Numbers: F33, G15, G20, O31.

Kristian R. Miltersen, Eduardo S. Schwartz, Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates, The Journal of Financial and Quantitative Analysis, Vol. 33, No. 1 (Mar., 1998), pp. 33-59