Add training workflow, datasets, and runbook

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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