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

The figure shows the estimated seasonal function ν(t) for the full-sample as well as the estimated
seasonal function for the first sub-period, ν 1 (t), and the estimated seasonal function
for the second sub-period, ν 2 (t). The estimated seasonal functions seem very similar with
amplitudes of similar magnitude and with minima and maxima attained at about the same
time of the year. The amplitude is slightly higher in the second sub-period and, if not simply
due to randomness, this could be due to the above-mentioned price floors maintained by the
US government programs up through the 1980s.
I Figure 5 we have similarly illustrated the seasonal patterns of the mean-reverting level of
the convenience yield as estimated in the first sub-period, α 1 (t), the second sub-period, α 2 (t),
as well as for the full sample, α(t).
[ INSERT FIGURE 5 ABOUT HERE ]
While the estimated functions attain minima and maxima at the same times of the year,
the amplitudes seem very different. However, though the amplitude for the first sub-period
estimation is much larger, it may be noted that the mean-reversion tendency is at the same
time much lower than for the second sub-period, as reflected in the β estimates. Hence, the
overall seasonal effect on the level of the convenience yield may not differ very substantially
across the two sub-periods.
Finally, it is seen from Table 4 and Table 5 that the estimated correlation coefficients (ρ 12 ,
ρ 13 , and ρ 23 ) are very similar across the two sub-periods. Thus, the conclusion that, e.g.,
convenience yields do not behave like timing options is robust over time since in both subperiods
the correlation coefficient, ρ 23 , between the convenience yield and volatility is close to
zero and, in fact, consistently estimated slightly negative. Also, the “inverse leverage effect” is
robust over time since the correlation coefficient, ρ 13 , between the spot price and the volatility
is consistently estimated positive and of the same magnitude across the sub-periods.
4 Conclusions
In the paper we have set up a stochastic volatility model of commodity price behavior and
estimated the model parameters using panel-data of both soybean futures and soybean options.
The estimation approach thus use the information in both time series characteristics of the
evolvement of soybean product prices as well as the information inherent in futures price
structures and option price structures, such as implied volatility surfaces.
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