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+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