Long-term futures prices would have value as price forecasts and as a way to structure long-term swaps and insurance contracts. However, the longest time to maturity for agricultural commodity futures is less than four years. Agricultural commodity markets generally exhibit mean reversion in spot prices and convenience yields. Spot markets also exhibit seasonality. We develop and implement a procedure to generate long-term futures curves from existing futures prices. Data on lean hogs and soybeans are used to show that the method provides plausible and statistically significant results.

Fair value of option premium is also affected by price mean reversion and seasonality. Standard option pricing models assume proportionality between price variance and time to maturity. This proportionality is not a valid assumption for commodities whose supply response brings prices back to production costs. The model proposed here incorporates mean reversion in price levels and includes a correction for seasonality. Our model suggests that the inappropriate use of these other models will result in overpricing of long-term options in renewable commodity markets. The empirical analysis lends strong support to our model.

We also investigate the relationship between futures price return volatility and the contract's time to maturity. The Samuelson hypothesis predicts that futures price return volatility will increase as the futures contract approaches its expiration date. In prior tests of this hypothesis, researchers have used linear regression to show this relationship generally holds. We develop a term structure model that predicts that this pattern is generally non-linear, if the Samuelson effect exists. We use data on ten commodities to test the hypothesis using our model and the linear model. The evidence suggests that our model can better explain the term structure of futures return volatility on metals, livestock and energy markets.