The gamma of the 37.50 call is about 72 percent that of the 35 call. But
the theta of the 37.50 call is about half that of the 35 call. Kim is improving
her gamma/theta relationship by buying the OTM, but with the call being so
far out-of-the-money and so inexpensive, the theta needs to be taken with a
grain of salt. It is ultimately gamma that will make or break this delta play.
The price of the option is 0.20—a rather low premium. In order for the
call to gain in value, delta has to go to work with help from gamma. At this
point, the delta is small, only 0.185. If Kim’s forecast is correct and there is
a big move upward, gamma will cause the delta to increase, and therefore
also the premium to increase exponentially. The call’s sensitivity to gamma,
however, is dynamic.
Exhibit 4.7 shows how the gamma of the 37.50 call changes as the stock
price moves over time. At any point in time, gamma is highest when the call
is ATM. However, so is theta. Kim wants to reap as much benefit from
gamma as possible while minimizing her exposure to theta. Ideally, she
wants Disney to rally through the strike price—through the high gamma
and back to the low theta. After three weeks pass, with 23 days until
expiration, if Disney is at $37 a share, the gamma almost doubles, to 0.237.
When the call is ATM, the delta increases at its fastest rate. As Disney rises
above the strike, the gamma figures in the table begin to decline.
EXHIBIT 4.7 Disney 37.50 call price–time matrix–gamma.