A simple equilibrium model for a commodity market with spot trades and futures contracts

Abstract

We propose a simple equilibrium model, where the physical market of the commodity and the derivative market interact. There are three types of agents: industrial processors, inventory holders and speculators. Only the two first of them operate in the physical market. All of them, however, may initiate a position in the paper market, for hedging and/or speculation purposes. We give the necessary and sufficient conditions on the fundamentals of this economy for a rational expectations equilibrium to exist and we show that it is unique. This is the first contribution of the paper. Our model exhibits a surprising variety of behaviours at equilibrium. Thus the second contribution is that the paper offers a unique generalized framework for the analysis of price relationships. The model allows for the generalization of hedging pressure theory; and it shows how this theory is connected to the storage theory. Meanwhile, it allows to study simultaneously the two main economic functions of derivative markets: hedging and price discovery. In its third contribution, through the distinction between the utility of speculation and that of hedging, the model illustrates the interest of a derivatives market in terms of the welfare of the agents.