Dynamic Gamma
When options are far in-the-money or out-of-the-money, they are either
1.00 delta or 0 delta. At the extremes, small changes in the stock price will
not cause the delta to change much. When an option is at-the-money, it’s a
different story. Its delta can change very quickly.
ITM and OTM options have a low gamma.
ATM options have a relatively high gamma.
Exhibit 2.6 is an example of how moneyness translates into gamma on
QQQ calls.
EXHIBIT 2.6 Gamma of QQQ calls with QQQ at $44.
With QQQ at $44, 92 days until expiration, and a constant volatility input
of 19 percent, the 36- and 54-strike calls are far enough in- and out-of-the-
money, respectively, that if the Qs move a small amount in either direction
from the current price of $44, the movement won’t change their deltas
much at all. The chances of their money status changing between now and
expiration would not be significantly different statistically given a small
stock price change. They have the smallest gammas in the table.
The highest gammas shown here are around the ATM strike prices. (Note
that because of factors not yet discussed, the strike that is exactly at-the-
money may not have the highest gamma. The highest gamma is likely to
occur at a slightly higher strike price.) Exhibit 2.7 shows a graph of the
corresponding numbers in Exhibit 2.6 .