734 Part VI: Measuring and Trading Volatillty 
Opt price = f(Stock price, Strike price, Time, Risk-free rate, Volatility, Dividends) 
Furthermore, suppose that one knows the following information: 
XYZ price: 52 
April 50 call price: 6 
Time remaining to April expiration: 36 days 
Dividends: $0.00 
Risk-free interest rate: 5% 
This information, which is available for every option at any time, simply from an 
option quote, gives us everything except the implied volatility. So what volatility 
would one have to plug in the Black-Scholes model ( or whatever model one is using) 
to make the model give the answer 6 (the current price of the option)? That is, what 
volatility is necessary to solve the equation? 
6 = f(52, 50, 36 days, 5%, Volatility, $0.00) 
Whatever volatility is necessary to make the model yield the current market price (6) 
as its value, is the implied volatility for the XYZ April 50 call. In this case, if you're 
interested, the implied volatility is 75.4%. The actual process of determining implied 
volatility is an iterative one. There is no formula, per se. Rather, one keeps trying var­
ious volatility estimates in the model until the answer is close enough to the market 
value. 
THE VOLATILITY OF VOLATILITY 
In order to discuss the implied volatility of a particular entity - stock, index, or 
futures contract one generally refers to the implied volatility of individual options 
or perhaps the composite implied volatility of the entire option series. This is gener­
ally good enough for strategic comparisons. However, it turns out that there might be 
other ways to consider looking at implied volatility. In paiticular, one might want to 
consider how wide the range of implied volatility is - that is, how volatile the indi­
vidual implied volatility numbers are. 
It is often conventional to talk about the percentile of implied volatility. That is 
a way to rank the current implied volatility reading with past readings for the same 
underlying instrument. 
However, a fairly important ingredient is missing when percentiles are involved. 
One can't really tell if "cheap" options are cheap as a practical matter. That's because 
one doesn't know how tightly packed together the past implied volatility readings are. 
For example, if one were to discover that the entire past range of implied volatility 
for XYZ stretched only from 39% to 45%, then a current reading of 40%, while low,