A maximal stochastic volatility model for commodity prices

Date of Completion

January 2007


Economics, Finance




The first essay develops and estimates an affine three-factor stochastic volatility model of commodity prices, where the instantaneous variance is driven by a single state variable. The model is maximal among all such models that are also identifiable. The model leads to closed-form formulas, up to numeric integration, 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. These properties are empirically documented for many commodities. Furthermore, the model nests all affine one- and two-factor Gaussian models of commodity prices, as well as the Heston (1993) model. I find that the model provides a much better fit to the observed crude oil futures prices than do these nested models.^ The question I address in the second essay is: Do Treasury bond yield data favor the Cox, Ingersoll, and Ross (CIR) model over the Vasicek model, or vice versa? While these two bond pricing models have been analyzed and estimated individually, there is no study - to my knowledge - that asks whether observed bond prices are more likely to be generated by one model versus the other. I investigate this question using the Bayesian approach to hypothesis testing. In particular, I compute the posterior odds ratio that the Vasicek model is more favorable than the CIR model, conditional only on the bond yield data. I find that Treasury bond yield data very strongly favor the CIR model over the Vasicek model.^