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I'm trying to figure out how the numbers in the "Model" and "Model IV" columns in the Options Chain viewer are calculated.
I have seen??but to me that's vague, I want some formulas.

To fix the ideas:?

S = underlying
K = strike
sigma = volatility
etc.

Let C(sigma) = price of a call, for a given K, S, etc. (ignoring the other variables). Suppose, a call trades for $10 on the exchange. Then, the implied volatility (for that option's maturity and strike) is?

sigma = C^{-1} (10).

i.e the volatility that would yield C = 10, when plugged in into the Black-Scholes formula. It's irrelevant, for the current discussion, how to compute IV numerically.

Now - I'm guessing - the "Model" column represents the option prices computed (for different strikes), using the implied volatility of a particular strike, most likely the at the money IV. That is, if sigma_0 is the IV of the at the money option, then the prices in the "Model" column are C(sigma_0, K, S, ... ) given by Black-Scholes. This is just my guess, it would be great if someone could confirm that that's what IB does.

For Model IV, however, I have no clue. It can't be implied volatility computed from the Model prices, because in then we'd get the same volatility across all strikes - namely the at the money implied volatility. And it can't be IV computed using the exchange prices (and Black-Scholes), because that would be the regular IV. So what is it?

Can anyone shed some light please? Thanks!

I suggest looking into the Newton-Raphson method to extract IV from quoted options prices.
You may also use Nelder-Mead if you consider the dividend yield as an additional unknown.
That said, the dividend yield effect topricing can be removed for European options so Newton-Raphson is sufficient for those.

Very useful pointers, thank you! I'm not trying to create my own option pricing model, just trying to understand what IB is computing.?