44 lines
2.2 KiB
Plaintext
44 lines
2.2 KiB
Plaintext
Chapter 40: Advanced Concepts
|
||
p2 = p 1 +delta+ gamma, or substituting from above
|
||
p2 = (p0 + delta) + delta + gamma
|
||
= Po + 2 x delta + gamma
|
||
6.04 = 5.00 + 2 x 0.505 + 0.03 (in the example if XYZ = 90)
|
||
875
|
||
By the same calculation, the put in the example will be priced at 4.04 if XYZ imme
|
||
diately jumps to 90:
|
||
4.04 = 5.00 - 2 X 0.495 + 0.03
|
||
So, overall, the call will have increased by 1.04, but the put will only have
|
||
decreased by 0.96. The unrealized loss would then be computed as -$10,400 for the
|
||
100 calls, offset by a gain of $9,600 on the sale of 100 puts, for a net unrealized loss
|
||
of $800. This verifies the result obtained above using position delta and position
|
||
gamma. Again, this confirms the logical fact that a quick stock movement will cause
|
||
unrealized losses in a short straddle position.
|
||
Continuing on, let us look at some of the other factors affecting the sale of this
|
||
straddle. The straddle seller has time working in his favor. After the position is estab
|
||
lished, there will not be as much decay in the first two-week period as there will be
|
||
when expiration draws near. The exact amount of time decay to expect can be calcu
|
||
lated from the theta of the position:
|
||
XYZ: 88
|
||
Position
|
||
Sold l 00 July 90 calls
|
||
Sold l 00 July 90 puts
|
||
Option
|
||
Theta
|
||
-0.03
|
||
-0.03
|
||
Position
|
||
Theta
|
||
+$300
|
||
+$300
|
||
+$600
|
||
This is how the position looked with respect to time decay when it was first
|
||
established (XYZ at 88 and three months remaining until expiration). The theta of the
|
||
put and the call are essentially the same, and indicate that each option is losing about
|
||
3 cents of value each day. Note that the theta is expressed as a negative number, and
|
||
since these options are sold, the position theta is a positive number. A positive posi
|
||
tion theta means time decay is working in your favor. One could expect to make $300
|
||
per day from the sale of the 100 calls. He could expect to make another $300 per day
|
||
from the sale of the 100 puts. Thus, his overall position is generating a theoretical
|
||
profit from time decay of $600 per day.
|
||
The fact that the sale of a straddle generates profits from time decay is not
|
||
earth-shattering. That is a well-known fact. However, the amount of that time decay |