hi rtrs111,
here's the way i see it. Feel free all, to correct me if i'm wrong.
We don't know the strike of the itm put, but presumably it can’t be much above the forward value of $ 60 + 8 at expiry (i.e. $68 growing at the risk free rate to expiry), or else i could, borrow $68, buy the stock and the put, exercise the put at expiry (is this a european option?), pay back the $68 + interest and walk off with the risk free profit = arbitrage. So let’s say it’s about $65.
Now, if you know that at expiry the stock’s going to be $1, you’ll make some $64 from the itm put (which cost you $8), and $1 from the otm put (which only cost 8 cents). From that point of view, the otm seems much more profitable.
If the stock price has collapsed to $1 (ouch!) by that time, then the vol’s not really going to mean too much for the itm put, since it is so deeply itm by that point. It’s delta is going to be about –1. For the (currently) otm one, that will now only just be itm, so the delta is going to be closer to –0.5. The vol absolutely matters for this one.
If the stock price is $1 by aug 10, if it’s american, exercise the hell out of it. The theta’s only going to work against you in that situation. If it’s european, the heavily itm put isn’t likely to change much in percentage terms, while the other one could go either way. It really does depend on the vol then to see which is better.
If you do have all the information needed for bs (i.e both vols), i guess you could plug in the numbers, and see which one is most ‘mispriced’ in the market in percentage terms relative to the vols you’ve used. You’d also need to balance that with your acceptance of risk (especially gamma and it’s ‘inverse’ theta), as has been mentioned here.
