A maximal affine stochastic volatility model of oil prices



This study develops and estimates a stochastic volatility model of commodity prices that nests many of the previous models in the literature. The model is an affine three-factor model with one state variable driving the volatility and is maximal among all such models that are also identifiable. The model leads to quasi-analytical formulas for futures and options prices. It allows for time-varying correlation structures between the spot price and convenience yield, the spot price and its volatility, and the volatility and convenience yield. It allows for expected mean-reversion in the short term and for an increasing expected long-term price, and for time-varying risk premia. Furthermore, the model allows for the situation in which options' prices depend on risk not fully spanned by futures prices. These properties are desirable and empirically important for modeling many commodities, especially crude oil. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:101–133, 2010