758 Part VI: Measuring and Trading Volatility 
direct manner. That is, an increase in implied volatility will cause the option price to 
rise, while a decrease in volatility will cause a decline in the option price. That piece 
of information is the most important one of all, for it imparts what an option trader 
needs to know: An explosion in implied volatility is a boon to an option owner, but 
can be a devastating detriment to an option seller, especially a naked option seller. 
A couple of examples might demonstrate more clearly just how powerful the 
effect of implied volatility is, even when there isn't much time remaining in the life 
of an option. One should understand the notion that an increase in implied volatility 
can overcome days, even weeks, of time decay. This first example attempts to quan­
tify that statement somewhat. 
Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3-
month call with striking price of 100. Furthermore, suppose that implied volatility is 
currently at 20%. Given these assumptions, the Black-Scholes model tells us that the 
call would be trading at a price of 4.64. 
Stock Price: 
Strike Price: 
Time Remaining: 
Implied Volatility: 
Theoretical Call Value: 
100 
100 
3 months 
20% 
4.64 
Now, suppose that a month passes. If implied volatility remained the same 
(20% ), the call would lose nearly a point of value due to time decay. However, how 
much would implied volatility have had to increase to completely counteract the 
effect of that time decay? That is, after a month has passed, what implied volatility 
will yield a call price of 4.64? lt turns out to be just under 26%. 
Stock Price: 
Strike Price: 
Time Remaining: 
Implied Volatility: 
Theoretical Call Value: 
100 
100 
2 months 
25.9% 
4.64 
What would happen after another month passes? There is, of course, some 
implied volatility at which the call would still be worth 4.64, but is it so high as to be 
unreasonable? Actually, it turns out that if implied volatility increases to about 38%, 
the call will still be worth 4.64, even with only one month of life remaining: