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+754 Part VI: Measuring and Trading Volatility 
+FIGURE 37-1. 
+Theoretical option prices at differing implied 
+volatilities (6-month calls). 
+80 
+70 
+Q) 60 
+(.) 
+·;::: 
+Cl.. 50 
+C: 
+0 
+·a 40 
+0 
+30 
+20 
+10 
+Stock Price 
+60 80 100 C 120 140 
+_JY.._ 
+170% 
+140% 
+110% 
+80% 
+50% 
+20% 
+The bottom line in Figure 37-1 (where implied volatility= 20%) has a distinct 
+curvature to it when the stock price is between about 80 and 120. Thus the delta 
+ranges from a fairly low number (when the stock is near 80) to a rather high number 
+(when the stock is near 120). Now look at the top line on the chart, where implied 
+volatility= 170%. It's almost a straight line from the lower left to the upper right! The 
+slope of a straight line is constant. This tells us that the delta (which is the slope) 
+barely changes for such an expensive option - whether the stock is trading at 60 or 
+it's trading at 150! That fact alone is usually surprising to many. 
+In addition, the value of this delta can be measured: It's 0. 70 or higher from a 
+stock price of 80 all the way up to 150. Among other things, this means that an out~ 
+of-the-money option that has extremely high implied volatility has a fairly high delta 
+- and can be expected to mirror stock price movements more closely than one might 
+think, were he not privy to the delta. 
+Figure 37-2 follows through on this concept, showing how the delta of an option 
+varies with implied volatility. From this chart, it is clear how much the delta of an 
+option varies when the implied volatility is 20%, as compared to how little it varies 
+when implied volatility is extremely high. 
+That data is interesting enough by itself, but it becomes even more thought-pro­
+voking when one considers that a change in the implied volatility of his option (vega) 
+also can mean a significant change in the delta of the option. In one sense, it explains 
+why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option 
+holder made nothing, because implied volatility declined from 170% to 140%.