Delta
Some of Kim’s risks warrant more concern than others. With this position,
delta is of the greatest concern, followed by theta. Kim expects the call to
rise in value and accepts the risk of decline. Delta exposure was her main
rationale for establishing the position. She expects to hold it for about three
weeks. Kim is willing to accept the trade-off of delta exposure for theta,
which will cost her three weeks of erosion of option premium. If the
anticipated delta move happens sooner than expected, Kim will have less
decay. Exhibit 4.3 shows the value of her 35 call at various stock prices
over time. The left column is the price of Disney. The top row is the number
of days until expiration.
EXHIBIT 4.3 Disney 35 call price–time matrix–value.
The effect of delta is evident as the stock rises or falls. When the position
is established (44 days until expiration), the change in the option price if the
stock were to move from $35 to $36 is 0.62 (1.66 − 1.04). Between stock
prices of $36 and $37, the option gains 0.78 (2.44 −1.66). If the stock were
to decline in value from $35 to $34, the option loses 0.47 (1.04 − 0.57). The
option gains value at a faster rate as the stock rises and loses value at a
slower rate as the stock falls. This is the effect of gamma.