754 Part VI: Measuring and Trading Volatility 
FIGURE 37-1. 
Theoretical option prices at differing implied 
volatilities (6-month calls). 
80 
70 
Q) 60 
(.) 
·;::: 
Cl.. 50 
C: 
0 
·a 40 
0 
30 
20 
10 
Stock Price 
60 80 100 C 120 140 
_JY.._ 
170% 
140% 
110% 
80% 
50% 
20% 
The bottom line in Figure 37-1 (where implied volatility= 20%) has a distinct 
curvature to it when the stock price is between about 80 and 120. Thus the delta 
ranges from a fairly low number (when the stock is near 80) to a rather high number 
(when the stock is near 120). Now look at the top line on the chart, where implied 
volatility= 170%. It's almost a straight line from the lower left to the upper right! The 
slope of a straight line is constant. This tells us that the delta (which is the slope) 
barely changes for such an expensive option - whether the stock is trading at 60 or 
it's trading at 150! That fact alone is usually surprising to many. 
In addition, the value of this delta can be measured: It's 0. 70 or higher from a 
stock price of 80 all the way up to 150. Among other things, this means that an out~ 
of-the-money option that has extremely high implied volatility has a fairly high delta 
- and can be expected to mirror stock price movements more closely than one might 
think, were he not privy to the delta. 
Figure 37-2 follows through on this concept, showing how the delta of an option 
varies with implied volatility. From this chart, it is clear how much the delta of an 
option varies when the implied volatility is 20%, as compared to how little it varies 
when implied volatility is extremely high. 
That data is interesting enough by itself, but it becomes even more thought-pro­
voking when one considers that a change in the implied volatility of his option (vega) 
also can mean a significant change in the delta of the option. In one sense, it explains 
why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option 
holder made nothing, because implied volatility declined from 170% to 140%.