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