Just curious: what do they use instead?Not exactly.
"Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula"
Authors: Espen Gaarder Haug, Nassim Nicholas Taleb


Everybody has his/her own opinion about what the price should be.who determines options prices and how they change as the underlying stock price changes? just curious.
Not exactly.
"Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula"
Authors: Espen Gaarder Haug, Nassim Nicholas Taleb
https://www.researchgate.net/public...e_Black-Scholes-Merton_Option_Pricing_Formula
https://nassimtaleb.org/2022/02/black-scholes-equation/
A somewhat imprecise but better answer would be "supply and demand, with market makers picking up the slack."
maybe few participants submit their bid/ask price without black scholes calculation, but by and large , cobe uses such modified model. I did a calc back in the days, only variations can be explained by different borrowing costs and volatility numbers, which are tailored to each participant. you can submit a wild spread but may not get filled.
Really? Where did those "volatility numbers" come from?
Tip: vol is backed out of the BSM (or whatever model you're using.) The formula can't give you a price without a vol figure; if you think it does, imagine a brand-new ticker and tell me how you're going to price it without any buyer/seller input. Or how the BSM will deal with buyers piling into a strike and progressively lifting the bid because there are no sellers.
Jump-diffusion model for short term volatility calc, but of course prop firm can always improve the data and submit a spread, or to make market.