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+854 Part VI: Measuring and Trading Volatility 
+Example: With XYZ at 49, assume the January 50 call has a delta of 0.50 and a 
+gamma of 0.05. If XYZ moves up one point to 50, the delta of the call will increase 
+by the amount of the gamma: It will increase from 0.50 to 0.55. 
+As with the delta, the gamma can also be expressed as a percentage. But in this 
+case, the increase or decrease applies to the delta. 
+Example: Again, with XYZ at 49, assume the January 50 call has a delta of 0.50 and a 
+gamma of 0.05. If XYZ moves up 2 points to 51, the delta of the call will increase by 
+5% of the stock rrwve, because the gamma is 0.05, or 5 percent. Five percent of the 
+stock move is 0.05 x 2, or 0.10. Thus, the delta will increase by 0.10, from 0.50 to 0.60. 
+Obviously, the delta cannot keep increasing by 0.05 each time XYZ gains anoth­
+er point in price, for it will eventually exceed 1.00 by that calculation, and it is known 
+that the delta has a maximum of 1.00. Thus, it is obvious that the gamma changes. In 
+general, the gamma is at its maximum point when the stock is near the strike of the 
+option. As the stock moves away from the strike in either direction, the gamma 
+decreases, approaching its minimum value of zero. 
+Conceptually, this means that a deeply in-the-money or deeply out-of-the­
+money option has a gamma of nearly zero. This makes sense - it implies that the delta 
+of a deep in- or deep out-of-the-money option does not change very much at all, even 
+if the stock moves by one point. 
+Example: Assume XYZ is 25, and the January 50 call has a delta of virtually zero. If 
+XYZ moves up one point to 26, the call is still so far out-of-the-money that the delta 
+will still be zero. Thus, the gamma of this call is zero, since the delta does not change 
+when the stock increases in price by a point. 
+In a similar manner, the January 45 put on XYZ would have a delta of -1.0 with 
+XYZ at 25. If XYZ moved up one point to 26, the put' s delta would not change; it is 
+still so far in-the-money that it would still be - 1.0. Thus, the gamma of this deeply 
+in-the-money option is also zero, since the delta remains unchanged in the face of a 
+I-point rise in the underlying security. 
+Note that the gamma of any option is expressed as a positive number, whether 
+the option is a put or a call. 
+Other properties of gamma are useful to know as well. As expiration nears, the 
+gamma of at-the-money options increases dramatically. Consider an option with a day 
+or two of life remaining. If it is at-the-money, the delta is approximately 0.50. 
+However, if the stock were to move 2 points higher, the delta of the option would jump