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+Chapter 40: Advanced Concepts 849 
+Let us now take a look at how both volatility and time affect the delta of a call 
+option. Much of the data to be presented in this chapter will be in both tabular and 
+graphical form, since some readers prefer one style or the other. 
+The volatility of the underlying stock has an effect on delta. If the stock is not 
+volatile, then in-the-money options have a higher delta, and out-of-the-money 
+options have a lower delta. Figure 40-1 and Table 40-1 depict the deltas of various 
+calls on two stocks with differing volatilities. The deltas are shown for various strike 
+prices, with the time remaining to expiration equal to 3 months and the underlying 
+stock at a price of 50 in all cases. Note that the graph confirms the fact that a low­
+volatility stock's in-the-money options have the higher delta. The opposite holds true 
+for out-of-the-money options: The high-volatility stock's options have the higher delta 
+in that case. Another way to view this data is that a higher-volatility stock's options will 
+always have more time value premium than the low-volatility stock's. In-the-money, 
+these options with more time value will not track the underlying stock price move­
+ment as closely as ones with little or no time value. Thus, in-the-money, the low­
+volatility stock's options have the higher delta, since they track the underlying stock 
+price movements more closely. Out-of-the-money, the entire price of the option is 
+composed of time value premium. The ones with higher time value (the ones on the 
+high-volatility stock) will move more since they have a higher price. Thus, out-of-the­
+money, the higher-volatility stock's options have the greater delta. 
+Time also affects delta. Figures 40-2 (see Table 40-2) and 40-4 show the rela­
+tionships between time and delta. Figure 40-2's scales are similar to those in Figure 
+40-2, delta vs. volatility: The deltas are shown for various striking prices, with XYZ 
+assumed to be equal to 50 in all cases. Notice that in-the-money, the shorter-term 
+options have the higher delta. Again, this is because they have the least time value 
+premium. Out-of-the-money, the opposite is true: The longer-term options have the 
+higher deltas, since these options have the most time value premium. 
+Figure 40-3 (see Table 40-3) depicts the delta for an XYZ January 50 call with 
+XYZ equal to 50. The horizontal axis in this graph is "weeks until expiration." Note 
+that the delta of a longer-term at-the-money option is larger than that of a shorter­
+term option. In fact, the delta shrinks more rapidly as expiration draws nearer. Thus, 
+even if a stock remains unchanged and its volatility is constant, the delta of its options 
+will be altered as time passes. This is an important point to note for the strategist, 
+since he is constantly monitoring the risk characteristics of his position. He cannot 
+assume that his position is the same just because the stock has remained at the same 
+price for a period of time. 
+Position Delta. Another usage of the term delta is what has previously been 
+referred to as the equivalent stock position (ESP); for futures options, it would be