Down/out puts are skewed on the index. Ask yourself why skew is persistent... i.e. cannot be arbed. You could have saved yourself weeks of self flagellation here.
I’m also trying to do things differently, but I’d just say that I don’t believe in your FairPUT approach or trying to replace BSM model. Your main issue is that everyone else uses BSM model (and its variants) so option prices are based on BSM or whatever other models, and you’ll have to adhere to prevailing prices in the market, not prices that you’d like to impose. Basically you won’t be able to sell something for $6 when everyone else will pay you $5. Or if an option cost $4 then you can spend $millions by buying them for $4 and thinking that it’s too cheap, but won’t be able to sell them later for $5 because no one will care what you think it’s worth. Therefore in my opinion a better approach would be to extract the pricing model out of the market and figure out how options are really priced (which may not be accurately based on BS but should align), not come up with your own model that is so unrelated to the market that it would require changing the market to make it work...
Use whatever model you want. It doesn't matter in vanilla vol. What is the difference between a put and a call? Underlying. The conversion mkt arbs strikes (boxes, rolls, etc.) and the model gives you a vol-line for relative value. If you (OP) were smart you'd work on a sticky-model, but you're not, and you're a noob.
@guru at all: I just want to create a correct option pricing model where CALL and PUT have the same payout. As said, I first tried it on the BSM, but failed miserably b/c that addition of mine to the BSM suddenly made arbitrage possible :-( So, this now is my 2nd attempt to find a solution. This means BSM can't be used for this desired option feature/behavior. The consequence is of course: I must find a new, independent option pricing model with that desired feature. I'm working on it and I'm confident to come up soon with a better model than BSM. It isn't that important for me whether the world will use my new model or not. I just want to create a mathematically correct option pricing model. History will decide about its success or failure: if it convinces the industry and the academics then the industry will abandon BSM and use that new pricing model. That's my simple plan.
In that case good luck. Just keep in mind that every industry punishes people who say “I want” vs “I did”. So do it first and then talk about it
Btw, my failed first attempt (applying the "FairPut" algorithm to BSM) is documented under this thread here at ET: https://www.elitetrader.com/et/thre...erivatives-market-how-to-profit-of-it.348911/
You don't understand synthetics. You don't understand arbitrage. If so, none of your threads would exist.
@destriero seems to make into his pants b/c he fears that with a fair option pricing model he will lose his secret cheating edge that the buggy BSM provides him. Of course it's his holy secret "edge"...