Revisiting the pricing of commodity futures and forwards

This article presents a collection of results and formulae for pricing commodity futures, futures options and forward contracts. These results extend previous work by Schwartz (1997). Unlike in Hilliard and Reis (1998), the model in this article predicts that jumps in the spot price affect futures and forward prices. Regime changes in the mean reversion level and in the volatility of spot prices also affect futures and forward prices. The discrete time setting, as the continuous time one, provides tractable pricing formulae, but it seems preferable to the continuous time setting for econometric estimation. In discrete time the market price of risk that affects futures and forwards can be more freely specified.