Thank you for your post and the link. May I ask you a couple of questions: 1. What sort of curves are they using? 2. Why I should ignore all ITM vols?
By put/call parity, ITMs and OTMs are the same thing (with put/call switched), and the OTMs typically have more volume and tighter pricing.
@truetype says it more succinctly than me, but this is what I was writing... 1) just a standard polynomial of the order of your preference (ivolatility paper does this). Sometimes piece-wise so that the polynomial is used out to a certain point and the wings are handled differently. That's about the most basic. There is a large literature on this. See for example SABR models. 2) the market for options is generally OTM so ITM option bid-ask spreads are wider. By put-call parity you can get one from the other anyway so just look at OTM (ok strictly this is only European options but...)
Regarding ITM & OTM IV. As Quiet1 has indicated; If the process is done properly, (PUT - CALL Parity is properly addressed), then the IV of the PUT and CALL at each strike will be identical, as well as OTM IV is used in place of ITM IV. -- the use of OTM over ITM may take some time/thought to sink in. For reasons unknown, to me, TOS does not do this correctly, but apparently most users do not require them to be accurate. (I think, if people really care, they do it themselves.)
Thank you for taking the time to answer my questions. Sorry, here is another question: I thought put-call parity refers to the relationship of put/call/interest/dividends for the same strike and expiry? You are saying I can extend this to corresponding OTM/ITM put/call switch? Regards,
To echo what the others have said... Most of the time the issues described occur with ITM options and with really really far out OTM ones. The other thing to check is whether you're computing the fwd correctly.
If you look at the wikipedia article on this you can see that you can re-arrange the formula to get from the value of a put to that of a call with the same strike/expiry (and vice versa).
I don't use ToS, but as Ghoul points out, the forward needs to be correct -- though that's a tautology, because the forward is just the price that equilibrates the put/call IVs at a given strike.
Agreed on correct algos on deriving the proper forwards! -- Deriving via marshaling the chains has been adequate for my purposes for Index options.