738 Part VI: Measuring and Trading Volatility 
FIGURE 36-4. 
$OEX implied versus historical volatility. 
10 
Implied minus Actual 1999 Date 
ity of $OEX options encompasses all the $OEX options, so it is different from the 
Volatility Index ($VIX), which uses only the options closest to the money. By 
using all of the options, a slightly different volatility figure is arrived at, as com­
pared to $VIX, but a chart of the two would show similar patterns. That is, peaks 
in implied volatility computed using all of the $OEX options occur at the same 
points in time as peaks in $VIX. 
(b) The actual volatility on the graph is a little different from what one normally 
thinks of as historical volatility. It is the 20-day historical volatility, computed 20 
days later than the date of the implied volatility calculation. Hence, points on the 
implied volatility curve are matched with a 20-day historical volatility calculation 
that was made 20 days later. Thus, the two curves more or less show the predic­
tion of volatility and what actually happened over the 20-day period. These actu­
al volatility readings are smoothed as well, with a 20-day moving average. 
(c) The difference between the two is quite simple, and is shown as the bottom 
curve on the graph. A "zero" line is drawn through the difference. 
When this "difference line" passes through the zero line, the projection of 
volatility and what actually occurred 20 days later were equal. If the difference line 
is above the zero line, then implied volatility was too high; the options were over­
priced. Conversely, if the difference line is below the zero line, then actual volatility 
turned out to be greater than implied volatility had anticipated. The options were 
underpriced in that case. Those latter areas are shaded in Figure 36-4. Simplistically, 
you would want to own options during the shaded periods on the chart, and would 
want to be a seller of options during the non-shaded areas.