Lets say I make a trade that consists of buying one put and 2 calls of the same underlying but with different expiration dates and different strikes.
Long call - strike @ $100 - exp 3/17/2015 Long put - strike @ $110 - exp: 3/30/2015 cost of trade = $15
Current price = $90, current date = 1/1/2015
If the trades expired on the same day the trade would net profit if the underlying price at expiration is greater than
$105. The probability of the trade being profitable would be equal to the probability of the underlying being above
$105 on the expiration date.
The trades unfortunately do not expire on the same day which complicates things. How do I calculate the probability of the trade being profitable when the options expire on different dates?
= (probability underlying > $105 @ 3/17/2015) * (probability underlying > $105 @ 3/30/2015)
I feel that the above is not correct as it does not account for the relationship between the two probabilities. Maybe a more correct equation would be:
= (probability underlying > $105 @ 3/17/2015) * (probability underlying > $105 starting from 3/17/2015 to 3/30/2015 with a starting price of $105)
Even this equation seems to be incorrect because if the option expires on the earlier date above the
$105, then it can expire below
$105 on the later expiration date.