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

This paper studies commodity spot, forward, and futures prices under a continuous-time setting. Our model considers a representative firm, which uses an input commodity to produce an output commodity, stores the commodity, and... [ view full abstract ]

This paper studies commodity spot, forward, and futures prices under a continuous-time setting. Our model considers a representative firm, which uses an input commodity to produce an output commodity, stores the commodity, and trades forward or futures commodities to hedge. Through the Hamilton-Jacobi-Bellman equation and Feynman-Kac formula, we derive relations between spot, forward, and futures prices. The convenience yield can be interpreted as shadow price of storage, short selling constraints, and limits of risk. We compare our result with the existing models. The optimal production plan and trading strategy for spot commodity and forward are also derived.