Get access

Long-term Futures Curves and Seasonal Structures of Wheat in the European Union and the United States


  • The views expressed are purely those of the authors and may not in any circumstances be regarded as stating an official position of the European Commission. We are grateful for the comments of the participants of two scientific seminars: the first “Modelling and Forecasting Agricultural Commodity Prices, A Special Focus on European Markets” at the European Commission, JRC, IPTS held in Sevilla, Spain on January 20–21, 2011 and the second “Modelling and Managing the Risks of Commodities and Food Prices” organized by the Commodity Finance Centre, University of London and held in London, UK on January 20, 2012.

Correspondence author, European Commission, JRC, IPTS, Ed. Expo c\ Inca Garcilaso 3, Sevilla 41092, Spain. Tel: +34 954 48 8458, Fax: +34 954 48 8434. e-mail:


A two-factor affine theoretical model is used to estimate the long-term futures curves for wheat in the European Union and the United States, as represented by the Euronext and CME markets, respectively. The CME futures curve exhibits a long-term equilibrium; in contrast, the Euronext futures curve does not show a tendency for futures to revert to a long-term equilibrium value. The estimated seasonality is relatively similar for both markets. However, the seasonal minimum and maximum points in the futures curve occur one to two months later for Euronext compared to the CME. More importantly, the futures curve for Euronext has a much more marked seasonality than the CME futures curve. Credible intervals of the futures curves are also estimated. The width clearly increases for longer maturities, but it does so much faster for Euronext than for the CME. For long-maturity futures, variability in the parameter estimates (as opposed to the residual errors) accounts for most of the width of the credible intervals, especially for Euronext. The proposed model can be used to price long-term futures options, long-term price insurance, and long-term swaps, among other applications. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:1118–1142, 2013