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training_data/relevant/text/fde8351491d1f3476bac4ffab0e48b63a5e862c32c8ae66396bea1cbb577b074.txt

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+904 Part VI: Measuring and Trading Volatility 
+Recall that, in the same example used to describe gamma, the position was delta 
+long 686 shares and had a positive gamma of 328 shares. Furthermore, we now see 
+that the gamma itself is going to decrease as the stock moves up ( it is negative) or will 
+increase as the stock moves down. In fact, it is expected to increase or decrease by 
+22 shares for each point XYZ moves. 
+So, if XYZ moves up by 1 point, the following should happen: 
+a. Delta increases from 686 to 1,014, increasing by the amount of the gamma. 
+b. Gamma decreases from 328 to 306, indicating that a further upward move by 
+XYZ will result in a smaller increase in delta. 
+One can build a general picture of how the gamma of the gamma changes over 
+different situations - in- or out-of-the-money, or with more or less time remaining 
+until expiration. The following table of two index calls, the January 350 with one 
+month of life remaining and the December 350 with eleven months of life remain­
+ing, shows the delta, gamma, and gamma of the gamma for various stock prices. 
+Index January 350 call December 350 call 
+Price Delta Gamma Gamma/Gamma Delta Gamma Gamma/Gamma 
+310 .0006 .0001 .0000 .3203 .0083 .0000 
+320 .0087 .0020 .0004 .3971 .0082 .0000 
+330 .0618 .0100 .0013 .4787 .0080 -.0000 
+340 .2333 .0744 .0013 .5626 .0078 -.0001 
+350 .5241 .0309 -.0003 .6360 .0073 -.0001 
+360 .7957 .0215 -.0014 .6984 .0067 -.0001 
+370 .9420 .0086 -.0010 .7653 .0060 -.0001 
+380 .9892 .0021 -.0003 .8213 .0052 -.0001 
+Several conclusions can be drawn, not all of which are obvious at first glance. 
+First of all, the gamma of the gamma for long-term options is very small. This should 
+be expected, since the delta of a long-term option changes very slowly. The next fact 
+can best be observed while looking at the shorter-term January 350 table. The 
+gamma of the gamma is near zero for deeply out-of-the-money options. But, as the 
+option comes closer to being in-the-money, the gamma of the gamma becomes a pos­
+itive number, reaching its maximum while the option is still out-of-the-money. By the 
+time the option is at-the-money, the gamma of the gamma has turned negative. It 
+then remains negative, reaching its most negative point when slightly in-the-money. 
+From there on, as the option goes even deeper into-the-money, the gamma of the 
+gamma remains negative but gets closer and closer to zero, eventually reaching 
+(minus) zero when the option is very far in-the-money.