I just overviewed this thread, and could see a lot of discussions about natural straddles and its two synthetics. Let us look at it from the short side with stock as underlying (no dividend to simplify things) assuming positive carry with american exercise. The three positions are:
A. -1p, and -1c
B. -2P-1S
C. -2C+1S.
Stock goes sufficiently down after option trading stops but before deadline to exercise (puts) is due. Your can assume a stock price move as large as you can to see the special cases where the difference may exist between the three positions.
The three positions are different from an exercise and carry point of views. For instance if a move down happens, I can cover position C with no problem by selling stock. If A, I still do not know if I should cover or not as the exercise of 1 put is not certain. If B, the problem is more pronounced as we have two short puts to deal with.
So Atticus seems to have had a good instinct when he mentioned sensitivity to price, but he seemed to have been put to deal with another issue.
When the price heads south the sum of the delta of the call and the absolute value of the put delta is no longer necessarily equal to 1, but a little bit more than 1. In addition a call will lose the vol premimum, but the put will compensate the vol premium by an exercise premium depending on the distance of the strike to the new stock price.
My question would be: how would you handle the three positions when you do not know whether you will be assigned or not on the short put and you want to deal with direction risk when stock tanks in A.H. (I assume that the use of AH earlier in this thread meant After Hours).