Commodity Spot, Forward, and Futures Prices with a Firm's Optimal Strategy

Author Name NAKAJIMA Katsushi (Ritsumeikan Asia Pacific University)
Creation Date/NO. February 2017 17-E-008
Research Project Economic and Financial Analysis of Commodity Markets
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This paper studies commodity spot, forward, and futures prices under a continuous-time setting. The model is an enhanced version of Nakajima (2015) which was modeled through discrete time. Our model considers a firm, which uses an input commodity to produce an output commodity, stores the commodity, and trades forwards 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 and conduct a numerical analysis. The optimal production plan and trading strategy for spot commodities and forwards are also derived. The model can be easily modified to consider cash settlement or hedging using output commodity forward contracts.