Option pricing model adjustments in practice

External question — Quantitative Finance Stack Exchange Author: Sam C Original post: https://quant.stackexchange.com/questions/79442 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I’m trying to understand significant differences in theoretical options pricing data that I‘m seeing. I’m new to this, so I suspect I’m missing something obvious. Taking a fixed set of inputs 1 , when I compute option price myself I get a roughly consistent value across a few methods (Black-Scholes, Bjerjsund-Stensland, binomial tree). I see similar results on some online options tools. But if I look at more professional tools like CBOE's LiveVol, the pricing data isn't close to the other values given the same inputs. The data my broker provides is also similar to CBOE. Basically all pricing data I can find or compute seems to cluster into two distinct groups and I can’t figure out why. With CBOE, they appear to be using Cox-Ross-Rubinstein given the API calls I see. What are they doing differently from when I run Cox-Ross-Rubinstein with the same inputs? Given their claim about using an "industry-standard binomial tree", I feel like I'm doing something wrong, not that the CBOE data is coming from a proprietary model. I've noticed the CBOE options pricing calculator uses the underlying security name as an input, and if I change this the pricing changes despite holding all other parameters ( 1 ) constant. Why would this be? Are they modifying my inputs before feeding them into the model? Thanks for the help! 1 Spot, strike, time to expiration, volatility, risk free rate; always American style calls and assuming no dividends