Commodity Spot, Forward Prices, and Convenience Yield Under Incomplete Market

Abstract

This paper analyzes the relation between commodity spot, forward prices, and convenience yield under incomplete markets. We show a financial pricing model of spot and forward commodity in an explicit fashion with production under incomplete markets and prove the existence of an equilibrium for this economy. One of the most important results of this paper is the difference between commodity spot and forward equilibrium price can be explained by the discounted shadow price of storage constraint minus the discounted marginal storage cost and it can be interpreted as the net convenience yield in the existing literature. Here the discounted factor is affected by the incompleteness of the markets. We prove the generic existence of the equilibrium and thus the obtained spot forward price relation is the equilibrium price formula. We also derive the firm's optimal production plan and trading strategy.