Chapter 37: How Volatility Affects Popular Strategies 
Stock Price: 
Strike Price: 
Time Remaining: 
Implied Volatility: 
Theoretical Call Value: 
100 
100 
1 month 
38.1% 
4.64 
759 
So, if implied volatility increases from 20% to 26% over the first month, then 
this call option would still be trading at the same price - 4.64. That's not an unusual 
increase in implied volatility; increases of that magnitude, 20% to 26%, happen all 
the time. For it to then increase from 26% to 38% over the next month is probably 
less likely, but it is certainly not out of the question. There have been many times in 
the past when just such an increase has been possible - during any of the August, 
September, or October bear markets or mini-crashes, for example. Also, such an 
increase in implied volatility might occur if there were takeover rumors in this stock, 
or if the entire market became more volatile, as was the case in the latter half of the 
1990s. 
Perhaps this example was distorted by the fact that an implied volatility of 20% 
is a fairly low number to begin with. What would a similar example look like if one 
started out with a much higher implied volatility - say, 80%? 
Example: Making the same assumptions as in the previous example, but now setting 
the implied volatility to a much higher level of 80%, the Black-Scholes model now 
says that the call would be worth a price of 16.45: 
Stock Price: 
Strike Price: 
Time Remaining: 
Implied Volatility: 
Theoretical Call Value: 
100 
100 
3 months 
80% 
16.45 
Again, one must ask the question: "If a month passes, what implied volatility 
would be necessary for the Black-Scholes model to yield a price of 16.45?" In this 
case, it turns out to be an implied volatility of just over 99%. 
Stock Price: 
Strike Price: 
Time Remaining: 
Implied Volatility: 
Theoretical Call Value: 
100 
100 
2 months 
99.4% 
16.45