Pricing and Hedging of Long-term Futures and Forward Contracts by a Three-Factor Model ( Revised in December 2007; Subsequently published in “Quantitative Finance”.)

Abstract

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. Moreover, it confirms that the prices of crude oil and copper futures prices estimated by our model replicate the observed ones very well.Finally, detailed performance analysis of hedging illiquid long-term futures and forwards with liquid short and medium-term futures shows the validity of our method.