Well I noticeably was made aware of how power IV is. I bought the Feb Put just cause I thought CSCO outlook would be bad and push the stock down alot, which it did. Because isn't it: If you buy a put option OTM say 2 weeks from expiration and an OTM option say 1month 2 weeks out, and the stock dropped 10%, wouldnt the front month option gain more?
You can explain it with deltas and gammas, but sometimes it's clearer to think about it qualitatively. If an option with two months to go is 10 points OTM, and suddenly the stock drops to 5 points OTM, the option will go up a couple bucks. The stock is getting closer to the money, and it is now much more conceivable that the stock will reach the strike price by expiration, making the option intrinsically worth something. If an option with two weeks to go is 10 points OTM, and suddenly the stock drops to 5 points OTM, now what? The stock still has a long way to go in two short weeks, to make the option worth anything at all. How likely are you to get a 5-point move in that short a time? Not much more likely than a 10-point move. So the option doesn't go up by much, because it's still more or less worthless. So, to answer your actual question, it depends how far OTM the option is.
As commiebat stated depends on how far OTM. A 1 strike OTM option I would say yes it would gain more, 2 strikes OTM maybe, 3 strikes OTM probably not.
1) What commmie_bat said 2) Two weeks before expiration, the delta of the 2nd month will be higher than the near month so it will gain more. The delta of the front month will get higher than the 2nd month when the underlying goes ITM and then it will gain more.