State-of-the-art term structure models of commodity prices have serious difficulties extrapolating the prices of long-maturity futures contracts from short-dated contracts. This situation is problematic for valuing real commodity-linked assets. We estimate a nonlinear four-factor continuous time model of commodity price dynamics. The model nests many previous specifications. To estimate the model, we use crude oil prices and inventories. The inventory data and nonlinear price dynamics have a large impact on oil price forecasts. The additional factor in our model compared with current three-factor models has a significant impact on model-implied long-maturity futures prices.

We develop equilibrium models of exhaustible resource markets with endogenous extraction choices and prices. Our analysis demonstrates how adjustment costs can generate oil and gas forward price dynamics with two factors, consistent with the behavior these commodities exhibit in the Schwartz and Smith (2000) calibration. Our two‐factor model predicts that stochastic volatility will arise in these markets as a natural consequence of production adjustments, however, and we provide supporting empirical evidence. Differences between endogenous price processes from our general equilibrium model and exogenous processes in earlier papers can generate significant differences in both financial and real option values.

State-of-the-art term structure models of commodity prices have serious difficulties extrapolating the prices of long-maturity futures contracts from short-dated contracts. This situation is problematic for valuing real commodity-linked assets. We estimate a nonlinear four-factor continuous time model of commodity price dynamics. The model nests many previous specifications. To estimate the model, we use crude oil prices and inventories. The inventory data and nonlinear price dynamics have a large impact on oil price forecasts. The additional factor in our model compared with current three-factor models has a significant impact on model-implied long-maturity futures prices.Received November 23, 2015; editorial decision September 12, 2016 by Editor Geert Bekaert.