Chapter 40: Advanced Concepts 855 
to nearly 1.00 because of the short time remaining until expiration. Thus, the gamma 
would be roughly 0.25 (the delta increased by 0.50 when the stock moved 2 points), 
as compared to much smaller values of gamma for at-the-money options with several 
weeks or months of life remaining. The same 2-point rise in the underlying stock 
would not result in much of an increase in the delta of longer-term options at all. 
Out-of-the-money options display a different relationship between gamma and 
time remaining. An out-of-the-money option that is about to expire has a very small 
delta, and hence a very small gamma. However, if the out-of-the-money option has a 
significant amount of time remaining, then it will have a larger gamma than the 
option that is close to expiration. 
Figure 40-4 (see Table 40-4) depicts the gammas of three options with varying 
amounts of time remaining until expiration. The properties regarding the relation­
ship of gamma and time can be observed here. Notice that the short-term options 
have very low gammas deeply in- or out-of the-money, but have the highest gamma 
at-the-money (at 50). Conversely, the longest-term, one-year option has the highest 
gamma of the three time periods for deeply in- or out-of-the-money options. The 
data is presented in Table 40-4. This table contains a slight amount of additional data: 
the gamma for the at-the-money option at even shorter periods of time remaining 
until expiration. Notice how the gamma explodes as time decreases, for the at-the­
money option. With only one week remaining, the gamma is over 0.28, meaning that 
the delta of such a call would, for example, jump from 0.50 to 0.78 if the stock mere­
ly moved up from 50 to 51. 
Gamma is dependent on the volatility of the underlying security as well. At-the­
money options on less volatile securities will have higher gammas than similar options 
on more volatile securities. The following example demonstrates this fact. 
Example: Assume XYZ is at 49, as is ABC. Moreover, XYZ is a more volatile stock 
(30% implied) as compared to ABC (20% ). Then, similar options on the two stocks 
would have significantly different gammas. 
XYZ Gammas ABC Gammas 
Option (Volatility = 30%) (Volatility= 20%) 
January 50 .066 .097 
January 55 .045 .039 
January 60 .019 .0053 
February 50 .055 .081 
February 60 .024 .011