Those probabilities are calculated from the Black-Scholes models that calculate greeks also, I think. That mean's they're an "approximation" for starters and secondly they assume brownian motion so a random possibility of the underlying moving higher or lower. For example the probability might read that with the underlying at $50 per share the $55 call has 60% probability of being ITM and the $45 put has 60% probability of being ITM (just making up number for the example). Using a normal-ish distribution this would be accurate, but stocks don't move in a completely random fashion, because people don't act in a completely random fashion. Thirdly, since the probabilities listed follow a normal or normal-ish distribution that means that there is a close-to-linear change in probability as you look at strikes further and further OTM. In reality in most cases if you have a stock at $50 the rate of change of probability from the $30 strike call to the $20 strike call (just making stuff up again, but think of a big move in the underlying like if the market crashes or the company gets acquired etc.) is not linear but might actually be the same or very nearly the same probability for the $30 and the $20 strike puts. Find another way. LOL.
So, I think the discussion so far can be summarized with: -- P(ITM) =/= delta -- Binomial P(ITM) =/= Normal P(ITM) =/= logNormal P(ITM) and that -- deep ITM/OTM probabilities are (to be kind) "fluffy" so, before we get too far afield (and, going back to the OP), here's two points more... -- binomial Ps and curvilinear Ps are not interchangeable. AND, -- one of the criticisms of Black/Scholes/Merton that actually merits some attention, is that it gets rather funky as time gets short. (And, this is where the binomial model(s) shine the better.) The OP does not specify the time horizon at work in the (anticipated set of the) question, so, a qualifier: "BSM 'P(ITM)' figures should be used with increasing caution, as expiration approaches."
I know you've just picked some random numbers... but can you try to be more accurate? With spot at 50, the 55 call having a 60% ITM prob isn't very likely, unless it's very high vol or a few years in maturity. But even if it is, than there's no way that the 45 put also has a 60% prob. They are both OTM... In theory, the ATM call and put both have 50% prob... everything OTM has a lower %. Also, the probabilities will follow a bell-curve across the strikes. That's because of the normal(-ish) distribution. So definitely not even close to linear. If you look at very far OTM, like your 20 and 30 puts, they seem very similar, because they will have a very small probability of ITM, depending on IV... but likely around 1% or less. In the bell-curve, those strikes are on the far tails, so yes... pretty linear.
Could you suggest any understandable read on how to calculate ITM/OTM Probs, POP, POT? My advanced mathematical grasp is very limited, hoping for something comprehensible. Any author who took the pain to explain it step-by-step from basics to advanced. Thank you!
One thing I learned a thousand years ago is that there are as many different styles of presentation as authors to present them. You've got to go out and find one yourself, whose presentation clicks for your brain. Nobody else's recommendations carry the approval of your own grey matter. (Been there, and payed for the t-shirt.)
Thanks for replying, Yes @tommcginnis, I am totally bewildered and confused with the amount of work shown by several authors. I don't know how to calculate POP/POT. And neither I am aware of the mathematical variations used for calculating ITM Prob%, which I think is the the mother of other probabilities. 100-ITM Prob% will tell us the probability of a strike expiring OTM. POT is approximately twice of ITM Prob% (not aware of the actual formula). Until I know what variations are used to discern ITM Prob% how will I figure out which one to use? I saw your above post # 1983 here and hoped for a place to start with. Many thanks!