The Dynamics of Commodity Spot, Forward, Futures Prices and Convenience Yield

This paper study commodity spot and futures price under a continuous-time setting. The model is an enhanced version of our earlier paper (2015) which was modeled through discrete time. Our model considers a firm, which use an input commodity to produce an output commodity, stores commodity, and trade futures commodity to hedge. Through dynamic programming principle and Hamilton-Jacobi-Bellman equation, we derive relations between spot price and futures price. The optimal production plan and trading strategy for spot commodity and futures are also derived. The model can be easily modified to consider cash settlement or hedging by ouput commodity futures. Our model can be generalized to include multiple firms which take multiple input commodities and multiple output commodities and multiple speculators.