Models for the price of a storable commodity
The current literature does not provide efficient models for commodity prices and futures valuation. This inadequacy is partly due to the fact that the two main streams of the literature - structural models and reduced form models - are largely disjoint. In particular, existing structural models are developed under rigid discrete time framework that does not take into account the mean-reverting properties of commodity prices. Furthermore, most of the literature within this class does not analyze the properties of the futures prices. Current reduced-form models allow cash-and-carry arbitrage possibilities and do not take into account the dependence between the spot price volatility and the inventory levels. This thesis investigates three new models for the price of a storable commodity and futures valuation. Specifically, we develop a structural model and two reduced-form models. In doing so, we expand the leading models within each of the two streams of the literature, by establishing a link between them. Each of these models provide an advance of their type. This study makes several contributions to the literature. We provide a new structural model in continuous time that takes into account the mean reversion of commodity prices. This model is formulated as a stochastic dynamic control problem. The formulation provided is flexible and can easily be extended to encompass alternative microeconomic specifications of the market. The results provide an optimal storage policy, the equilibrium prices and the spot price variability. We also develop a numerical method that allows the construction and analysis of the forward curves implied by this model. We provide a separate analysis considering a competitive storage and considering a monopolistic storage. The results are consistent with the theory of storage. Furthermore, the comparison between monopoly and competition confirm the economic theory. We developed a simple reduced-form model that focuses both on the mean reverting properties of commodity prices and excludes cash-and-carry arbitrage possibilities. This model is compared with a standard single-factor model in the literature. This new model adds two important features to the standard model and motivates the development of a more sophisticated reduced-form model. Accordingly, the last model developed in this thesis is a reduced-form model. It is a two-factor model that represents the spot price and the convenience yield as two correlated stochastic factors. This model excludes cash-and-carry arbitrage possibilities and takes into account the relationship between the spot price volatility and the inventory level. We find an analytical solution for the futures prices. This model is tested empirically using crude oil futures data and it Is compared with one of the leading models in the literature. Both models are calibrated using Kalman filter techniques. The empirical results suggest that both models need to be improved in order to better fit the long-term volatility structure of futures contracts.