A Simple Equilibrium Model for a Commodity Market with Spot and Futures Trades



Ivar Ekeland, Delphine Lautier, Bertrand Villeneuve

We propose a simple equilibrium model, where the physical and the derivative markets of the commodity 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. The model exhibits a surprising variety of behaviours at equilibrium; the second contribution is that we propose a unique generalized framework for the analysis of price relationships. The model indeed allows for the generalization of the normal backwardation theory and shows how it 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, the model illustrates what happens in a derivative market when speculation increases.

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