24 lines
1.6 KiB
Plaintext
24 lines
1.6 KiB
Plaintext
Each $1 increase in the stock shows an increase in the call value about
|
||
equal to the average delta value between the two stock prices. If the stock
|
||
were to decline, the delta would get smaller at a decreasing rate.
|
||
As the stock price declines from $60 to $59, the option delta decreases
|
||
from 0.50 to 0.46. There is an average delta of about 0.48 between the two
|
||
stock prices. At $59 the new theoretical value of the call is 2.52. The
|
||
gamma continues to affect the option’s delta and thereby its theoretical
|
||
value as the stock continues its decline to $58 and beyond.
|
||
Puts work the same way, but because they have a negative delta, when
|
||
there is a positive stock-price movement the gamma makes the put delta
|
||
less negative, moving closer to 0. The following example clarifies this.
|
||
As the stock price rises, this put moves more and more out-of-the-money.
|
||
Its theoretical value is decreasing by the rate of the changing delta. At $60,
|
||
the delta is −0.40. As the stock rises to $61, the delta changes to −0.36. The
|
||
average delta during that move is about −0.38, which is reflected in the
|
||
change in the value of the put.
|
||
If the stock price declines and the put moves more toward being in-the-
|
||
money, the delta becomes more negative—that is, the put acts more like a
|
||
short stock position.
|
||
Here, the put value rises by the average delta value between each
|
||
incremental change in the stock price.
|
||
These examples illustrate the effect of gamma on an option without
|
||
discussing the impact on the trader’s position. When traders buy options,
|
||
they acquire positive gamma. Since gamma causes options to gain value at |