Stochastic Volatility and Seasonality in ... - Interconti, Limited

a seasonality feature the long-run level for the convenience yield process would thus be 0.0751
(= α 0 /β); we interpret this as the “normal” level of the convenience yield when adjusted for
seasonality.
The seasonal pattern of the mean-reverting level of the convenience yield is also illustrated
in Figure 3. The seasonal variation in α(t) is very similar to the seasonal variation in ν(t),
though amplitudes are different. However, it is much more clear that α(t) has two local maxima
and two local minima. 16 Again, the global maximum is achieved in July about two months
prior to the beginning of the US harvesting while the global minimum is achieved and the end
of the US harvesting. While the US soybean production accounts for 50-60% of world soybean
production other key producers are Argentina and, especially, Brazil which are both located
in the Southern Hemisphere. These countries account together for 20-30% of world soybean
production. The Brazilian soybean harvesting takes place in March and April and the local
maximum in Figure 3 is reached about two months earlier, while the local minimum is reached
during the ending of the Brazilian soybean harvesting. The seasonal pattern in convenience
yields is thus related to the supply of soybeans. When supplies are low convenience yields are
high, and vice versa. This is consistent with the theory of storage which predicts a negative
relationship between inventories and convenience yields. The basic idea is that the holding of
physical inventory of soybeans gives rise to a convenience yield from being able to profit from
temporary soybean supply shortages or keep a production process running especially when
inventories are low. Furthermore, the parameter estimates suggest that the soybean spot price
and the convenience yield are positively correlated with a correlation coefficient of 0.3979.
Following the above kind of reasoning, this is also consistent with the observation that when
supplies and inventories are scarce the equilibrium soybean spot price and the convenience
yield are simultaneously high; and vice versa when supplies and inventories are plenty.
On the other hand, supporters of the theory of storage often view the convenience yield as
an option to profit from temporary shortages of the particular commodity. This would suggest
a positive correlation between the convenience yield and the volatility; however, this view is
not supported by the parameter estimate of ρ 23 which is not significantly different from zero
and even estimated negative.
16 The global maximum of the seasonal function α(t) is reached on July 15 where the function value is 0.746,
while the global minimum is reached on October 30 where the function value is -0.723. A local maximum is
reached on February 7, and a local minimum is reached on April 16.
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