The Intelligent Investor’s Guide to Option Pricing  •  63
With this change in assumptions, we can see that the most likely 
range for the stock’s price three years in the future is between about $50 and 
about $70. As such, the chance of the stock price hitting $70 in two years 
moves from somewhat likely (20 percent volatility in the first example) to 
very likely (40 percent volatility in the second example) to very unlikely 
(10 percent volatility in the third example) in the eyes of the BSM. This 
characterization of “very unlikely” is seen clearly by the fact that the BSM 
probability cone contains not one whit of the call option’s exposure range.
In each of these cases, we have drawn the graphs by first picking an 
assumed volatility rate and then checking the worth of an option at a cer -
tain strike price. In actuality, option market participants operate in reverse 
order to this. In other words, they observe the price of an option being 
transacted in the marketplace and then use that price and the BSM model 
to mathematically back out the percentage volatility implied by the option 
price. This is what is meant by the term implied volatility and is the process 
by which option prices themselves display the best guesses of the option 
market’s participants regarding forward volatility. 
Indeed, many short-term option speculators are not interested in the 
range of stock prices implied by the BSM at all but rather the dramatic change in 
price of the option that comes about with a change in the width of the volatility 
cone. For example, a trader who saw the diagram representing 10 percent annu-
alized forward volatility earlier might assume that the company should be trad-
ing at 20 percent volatility and would buy options hoping that the price of the 
options will increase as the implied volatility on the contracts return to normal.
This type of market participant talks about buying and selling volatility as if 
implied volatility were a commodity in its own right. In this style of option trad-
ing, investors assume that option contracts for a specific stock or index should 
always trade at roughly the same levels of implied volatility.
5 When implied vola-
tilities change from the normal range—either by increasing or decreasing—an 
option investor in this vein sells or buys options, respectively. Notice that this 
style of option transaction completely ignores not only the ultimate value of the 
underlying company but also the very price of the underlying stock. 
It is precisely this type of strategy that gives rise to the complex short-
term option trading strategies we mentioned in Chapter 1—the ones that are 
set up in such a way as to shield the investor transacting options from any of 
the directionality inherent in options. Our take on this kind of trading is that