Deterministic Seasonality Effects

Seasonality in price movements and volatility is an important difference between certain commodity classes and standard financial assets. Especially for agricultural commodities, one observes a repeating cyclical pattern of decreasing prices at the harvesting period and after the harvest and a peak in prices a few months before the harvest. Empirically, one can observe the seasonality in the term structure of futures prices for agricultural goods such as wheat or soybeans. While agricultural and animal products do show a seasonality effect, other groups of commodities such as metals or other raw materials do not.1 Furthermore, electricity futures prices share both a mean reverting and a seasonal property, due to the cyclical behavior of consumption which is mainly driven by the seasonal evolution of temperatures.2 The case of soybeans is investigated by Richter and Sørensen (2002), who model the soybean price process with subordinated stochastic volatility and convenience yield processes. They incorporate seasonality in the convenience yield process. The price process is not mean-reverting and the seasonality effect makes an indirect impact on prices through the convenience yield process and through a seasonal impact of volatility. Richter and Sørensen provide an empirical survey with a parameter estimation based on soybean futures and options on futures prices.