No, z is the "z-value" (calculated from volatility, spot, and strike) from probability calculations, p(z) is the probability belonging to that z-value, and S2K is simply the %distance of the underlying spot (S) to the strike (K).
@marsman..with all do respect, I think you have to get your OTM vs ITM straight in your head before working on the probabilities !
@marsman , ( sorry, didn't mean to sound so snarky in my previous) also I think I get where you are going with your "formula" but, is there a directional component to it ? or just distance in either direction from an ATM strike ?
I think there would probably be more of a market for and less early exercise of very deep in the money options if the margin rule for a simple long option position were changed from... 100% of the value of the option (at least that is my understanding of how it is in the United States) ...to... minimum(100% of value of the option, margin requirement of the underlying) The fact that a deep in the money option can have margin requirements exceeding the underlying creates an artificial incentive for early exercise or not to buy the option at all, and I don't see what the extra margin requirement protects anyone from in this case. Corrections and counterarguments are welcome.
No dir comp, yes in either dir... And of course use fabs(x)... In my case it's usually about finding high prob for _not_ happening a certain event... And from my experience: calculating the ITM and OTM values for _short_ positions is the most complicated (sometimes one needs them indeed)...
You could be right, indeed. The ITM part should be substracted from the 100% as it already is a collateral.
@marsman...be careful if you are just selling premium (even in spreads) based on probability and fabs without encorporating an opinion/call on the direction of the underlying and/or direction of vol. These risks have been discussed extensively in this forum.
The goal is to have the option of the holder expire worthless. Ie. keeping the position till it expires, not trying to early-close it. Then in fact volatility-change doesn't matter at all .