Chapter 37: How Volatility Affeds Popular Strategies 
TABLE 37-3 
Implied 
Stock Price Volatility 
50 10% 
30% 
50% 
70% 
100% 
150% 
200% 
Theoretical 
Coll Price 
1.34 
3.31 
5.28 
7.25 
10.16 
14.90 
19.41 
753 
Vega 
0.097 
0.099 
0.099 
0.098 
0.096 
0.093 
0.088 
of a 6-month call option with differing implied volatilities. Suppose one buys an 
option that currently has implied volatility of 170% (the top curve on the graph). 
Later, investor perceptions of volatility diminish, and the option is trading with an 
implied volatility of 140%. That means that the option is now "residing" on the sec­
ond curve from the top of the list. Judging from the general distance between those 
two curves, the option has probably lost between 5 and 8 points of value due to the 
drop in implied volatility. 
Here's another way to think about it. Again, suppose one buys an at-the-money 
option (stock price = 100) when its implied volatility is 170%. That option value is 
marked as point A on the graph in Figure 37-1. Later, the option's implied volatility 
drops to 140%. How much does the stock have to rise in order to overcome the loss 
of implied volatility? The horizontal line from point A to point B shows that the 
option value is the same on each line. Then, dropping a vertical line from B down to 
point C, we see that point C is at a stock price of about 109. Thus, the stock would 
have to rise 9 points just to keep the option value constant, if implied volatility drops 
from 170% to 140%. 
IMPLIED VOLATILITY AND DELTA 
Figure 37-1 shows another rather unusual effect: When implied volatility gets very 
high, the delta of the option doesn't change much. Simplistically, the delta of an 
option measures how much the option changes in price when the stock moves one 
point. Mathematically, the delta is the first partial derivative of the option model with 
respect to stock price. Geometrically, that means that the delta of an option is the 
slope of a line drawn tangent to the curve in the preceding chart.