Risk Premia and Seasonality in Commodity Futures

​We develop and estimate a multifactor affine model of commodity futures that allows for stochastic variations in seasonality. We show conditions under which the yield curve and the cost-of-carry curve adopt augmented Nelson and Siegel functional forms. This restricted version of the model is parsimonious, does not suffer from identification problems, and matches well the yield curve and futures curve over time. We estimate the model using heating oil futures prices over the period 1984–2012. We find strong evidence of stochastic seasonality in the data. We analyse risk premia in futures markets and discuss two traditional theories of commodity futures: the theory of storage and the theory of normal backwardation. The data strongly supports the theory of storage