858 Part VI: Measuring and Trading Volatility 
FIGURE 40-5. 
Gamma comparison, with XYZ = 50, t = three months. 
8 
7 
0 6 
0 
~ 5 
<ti 
E 4 E 
~ 3 
2 
TABLE 40-5. 
40 45 
Low Volatility 
Very High Volatility 
50 55 60 
Strike Price 
65 
Gamma comparison for varying volatilities (XYZ = 50, t = 3 
months). 
Gamma Very 
Strike Low Volatility High Volatility High Volatility 
40 .003 .013 .017 
45 .039 .039 .022 
50 .086 .057 .024 
55 .057 .049 .025 
60 .015 .028 .023 
65 .002 .012 .020 
As before, the position still has a delta long of almost 700 shares. In addition, 
one can now see that it has a positive gamma of over 300 shares. This means that the 
delta can be expected to change by 328 shares for each point that XYZ moves: If it 
moves up 1 point, the delta will increase to +1,014 (the current delta, 686, plus the 
gamma of 328). However, ifXYZ moves down by 1 point, then the delta will decrease 
to +358 (the current delta, 686, less the gamma of 328). 
Note that, in the above example, if XYZ continues higher, the gamma will 
remain positive (although it will eventually shrink some), and the delta will continue 
to increase. This means the position is getting longer and longer - a fact that makes