Pricing and Hedging of Long-Term Futures and Forward Contracts by a Three-Factor Model

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. It also examines the relation of our model with Schwartz(1997) type models that explicitly include interest rates and convenience yields. Then, it is confirmed that the prices of crude oil and copper futures prices estimated by our model replicate the observed ones quite well. Finally, detailed performance analysis of hedging long-term futures and forwards with short-term futures are presented, which shows the validity of our method.