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We introduce a multi-factor stochastic volatility model for commodities thatincorporates seasonality and the Samuelson effect. Conditions on the seasonalterm under which the corresponding volatility factor is well-defined are given,and five different specifications of the seasonality pattern are proposed. Wecalculate the joint characteristic function of two futures prices for differentmaturities in the risk-neutral measure. The model is then presented under thephysical measure, and its state-space representation is derived, in order toestimate the parameters with the Kalman filter for time series of corn, cotton,soybean, sugar and wheat futures from 2007 to 2017. The seasonal modelsignificantly outperforms the nested non-seasonal model in all five markets,and we show which seasonality patterns are particularly well-suited in eachcase. We also confirm the importance of correctly modelling the Samuelsoneffect in order to account for futures with different maturities. Our resultsare clearly confirmed in a robustness check carried out with an alternativedataset of constant maturity futures for the same agricultural markets.

Seasonal Stochastic Volatility and the Samuelson Effect in Agricultural Futures Markets