This applies to all options, but using an example: NVDA is at 13.5. DITM SEPT 45P at $31, has an IV of ~188% I am really confused about this. I understand what standard deviation is, but in this context it's basically saying the 45P has a 68% chance of staying between ($31-$55) and ($31+$55) range by sept expiration(of course it will!). And gets even more ridculus as you increase to 2 std. Why are the IV so high for DITM contracts? I have a feeling it's one of those things that will make perfect sense once you see it, but i just dont.

You got it wrong. The "price" for the DITM 45 put would approx midway between the bid and ask. Which, subtracted from the strike would give you current price of the stock plus the small amount of interest you'd receive. There could be 188% IV for NVDA options but is irrelevant for ~1.0 delta

Forget about the puts for a moment, and look at those calls. From the 22.5 calls all the way up to the 45's, they all are 0 bid at .05. Now, the 22.5 calls are maybe legitimately 0 bid at .05 - meaning there's a prayer someone will pay .05 for them. But clearly there is NO prayer someone will pay .05 for the 25 calls right? Why would they if they can buy the 22.5 calls there? The 45 calls? Forget about them. Of course they're offered at .05 technically - nobody's going to offer them at 0 - but that is completely meaningless. However, the implied volatility of every call from 22.5 to 45 is computed using the "in-between" price of .025 - even though that price is completely fictitious for every call above 22.5. If you calculate the implied volatility of the 45 call using a price of .025, you get an implied volatility of 172%. Of course, that does NOT imply anything about probable volatility in the underlying. If there were strikes up to 100, the 100 calls would probably have an implied volatility of over 500%. Completely meaningless.

DMO, that makes perfect sense for OTM call. But i am still a bit confused in the case of DITM put, the prices are not junk 0/0.5, they do scale up per the strike with a tight bid/ask. Are you saying basically once the delta becomes 0.98+, IV loses its meaning/usefulness as it basically becomes the underlying.

The price of an ITM put is composed of its intrinsic value (strike minus price of the underlying) plus time value. For the purposes of calculating IV, only the time value is used. Interest rate considerations aside, the time value of the 45 put should equal the price of the 45 call, since the 45 call has no intrinsic value. In other words, imagine the underlying is trading at 15, and the 45 put is 30 bid at 30.05. That means your pricing model is looking at a price of 30.025. Your pricing model lops off the 30 points of intrinsic value, and looks only at the remaining .025 of time value. So we're back to exactly where we were with the 45 call. Newguy, if this is still puzzling to you, your next assignment is to study put/call parity and time value and the relationship of puts and calls at the same strike until you know and believe and understand in the marrow of your bones that a put and a call at the same strike are exactly the same thing (except for the minor matter of their deltas - which is the most superficial property of an option and easily adjusted by buying or selling the underlying).

DMO, you are an endless well of option knowledge this is very clear now. Thank you I understood your first post on the otm call, and studied about the put/call parity a while back, but couldnt connect the two together.

BTW - going back to the discussion of the NVDA 45 calls - that is why the VIX calculation includes every SPX option "with a bid greater than zero." That simple filter eliminates the distorting effect of SPX options too far OTM to trade (the SPX equivalent of those NVDA 45 calls).