874 Part VI: Measuring and Trading Volatility 
FIGURE 40· 1 O. 
Proiected delta, in 14 days. 
6000 
4500 
3000 
Cl) 1500 ~ ro .c 
(/) 
0 'E 
(1) 
80 85 ~ ·5 -1500 
95 
XYZ Stock Price 
C" 
UJ 
-3000 
-4500 
Using the example data: 
Loss, XYZ moves from 88 to 89: -$100 (the position delta) 
Loss, XYZ moves from 89 to 90: -$100 (delta) - $600 (gamma) 
: -$700 
Total loss, XYZ moves from 88 to 90: -$100 x 2 - $600 = -$800 
This can be verified by looking at the prices of the call and put after XYZ has jumped 
from 88 to 90. One could use a model to calculate expected prices if that happened. 
However, there is another way. Consider the following statements: 
If the stock goes up by 1 point, the call will then have a price of: 
p 1 = Po + delta 
5.505 = 5.00 + 0.505 (if XYZ goes to 89 in the example) 
If the stock goes up 2 points, the call will have an increase of the above amount 
plus a similar increase for the next point of stock movement. The delta for that sec­
ond point of stock movement is the original delta plus the gamma, since gamma tells 
one how much his delta is going to change.