Competitive Storage and Commodity Price in Continuous Time

The competitive storage model is analyzed in the literature in discrete time and is applied for empirical studies of the markets for agricultural commodities. In this model, there is a storable commodity supplied at every period with stochastic disturbances, and there are traders who aim at making speculative profits by using their storage. The literature has established results such as the existence of an equilibrium price function, which depends on the current availability of the commodity. The present article proposes an extension to the competitive storage model by considering continuous time. The relevance of this extension is justified by the technical convenience it brings, as well as by its suitability to the mineral markets in which the time series data is available for daily frequency. I consider serially correlated disturbances of net supply together with an upper bound on storage capacity, and characterize the equilibrium price function in this framework. The no-arbitrage and no-trade conditions define the intertemporal choice of commodity traders and imply the existence of an equilibrium price function. The equilibrium price depends on "the long-term availability of commodity" defined as the sum of storage and the expected cumulative disturbances of net supply over the infinite horizon. The various cases of the equilibrium price dynamics, such as "full storage", "empty storage" and "the trading zone", are characterized. The two types of the equilibrium price function, which are relevant to full storage, are revealed, and an explicit approximate solution for the case of a low-elastic net demand is derived. Numerical simulations of the equilibrium price function demon­strate the effects of the model parameters on this function.