I kind of suspected this is what you were asking rather than anything to do with the "mid of the posted bid/ask". I doubt you'll learn anything meaningful by pursuing this "theo value" garbage because doing so means you found a mechanical method for computing the "correct" current IV based on something other than current market price and that's a slippery road to go down. Whether current IV is correct or not is known only in hindsight and not something found in a mechanical computation. I know of at least two vendors who sell services and software to compute such values but Iâm sure they earn more from vending it than from trading it.
Theo is a guy who comes down to the exchange floor once a week and sets the fair values for all the options. Theo=theoretical