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+Chapter 40: Advanced Concepts 857 
+delta will be more dramatic than it would be for a volatile stock. Out-of-the-money 
+options are an entirely different story. Since the nonvolatile stock will have difficulty 
+moving fast enough to reach an out-of-the-money striking price, the delta of the out­
+of-the-money option is small and it will not change quickly (that is, the gamma is 
+small also). 
+These concepts are summarized in Figure 40-5 (see Table 40-5), which depicts 
+the gammas for similar options on stocks with differing volatilities. For the purposes 
+of these graphs, XYZ is equal to 50 and there are three months remaining until expi­
+ration. 
+Notice that for a very volatile stock, the gamma is quite stable over nearly all 
+striking prices when there are 3 months remaining until expiration. This means that 
+the deltas of all options on such a volatile stock will be changing quite a bit for even 
+a 1-point move in the underlying stock. This is an important point for neutral strate­
+gists to note, because a position that starts out as delta neutral may quickly change if 
+the underlying stock is very volatile. As this table implies, the deltas of the options in 
+that "neutral" spread may be altered quickly, thereby rendering the spread quite un­
+neutral. This concept will be discussed in greater detail later in this chapter. 
+As delta was used to construct the equivalent stock position of an entire option 
+position or portfolio, gamma can be used in a similar manner. An example of this fol­
+lows, using the same securities from the preceding example on the delta of a posi­
+tion. An important point to note is that the gamma of the underlying security itself is 
+zero. This is true because the delta of the underlying security (which is always 1.0) 
+never changes - hence the gamma is zero. The gamma is measuring the amount of 
+change of the delta; if the delta of the underlying security never changes, the gamma 
+of the underlying security must be zero. 
+Example: The following position exists when XYZ is at 31.75. Recall that it resem­
+bles a long straddle ( or backspread) in that there is increased profit potential in either 
+direction if the stock moves far enough by expiration. In addition to the delta previ­
+ously listed, the gamma is now shown as well. Note that since gamma is a small 
+absolute number, it is sometimes calculated out to three or four decimal places. 
+Option Position Option Position 
+Position Delta Delta Gamma Gamma 
+Short 4,500 XYZ 1.00 - 4,500 0.0000 0 
+Short l 00 XYZ April 25 calls 0.89 - 8,900 0.0100 -100 
+Long 50 XYZ April 30 calls 0.76 + 3,800 0.0300 +150 
+Long 139 XYZ July 30 calls 0.74 +10,286 0.0200 +278 
+Totals: + 686 +328