Stochastic behavior of spot and futures commodity prices: Theory and evidence

This dissertation examines the stochastic behavior of commodity prices from two alternative approaches. The first chapter develops a three-factor Gaussian model of commodity spot prices, convenience yields and interest rates. Our model allows convenience yields to be a function of the spot price and interest rates. Also, it allows for time-varying risk-premia. For crude oil and copper we find strong evidence for spot-price level dependence in convenience yields, which implies mean-reversion in spot prices under the risk-neutral measure, and is consistent with the "theory of storage." For silver, gold and copper we find evidence for time-varying risk-premia, which implies mean-reversion of commodity prices under the physical measure albeit with different strength and long-term mean. The model thus disentangles the different sources of mean-reversion in spot commodity prices. The spot-price level dependence in convenience yields has a substantial impact for option prices, while the time-varying risk-premia affect risk management decisions. The second chapter examines commodity prices in a structural framework. In our model production of the consumption good requires two inputs: the consumption good and a oil. Oil is produced by wells whose flow rate is costly to adjust. Investment in new Oil wells is costly and irreversible. As a result in equilibrium, investment in Oil wells is infrequent and lumpy. The resulting equilibrium oil price exhibits mean-reversion and heteroscedasticity. The spot oil price is not Markov (in itself) and is best described as a regime-switching process. The futures curve exhibits backwardation as a result of a convenience yield, which arises endogenously due to the productive value of oil as an input for production. The model is capable of matching the first two moments of the futures curves and the average consumption of oil-output and output-consumption ratios from macroeconomic data.