Option Traders never use the Black–Scholes–Merton Formula.
We have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a
well known (and used) formula compatible with the economics establishment, by removing the “risk” parameter through “dynamic
hedging”, (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the
previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and
removed the risk parameter using put-call parity, (3) option traders did not use the Black–Scholes–Merton formula or similar formulas
after 1973 but continued their bottom-up heuristics more robust to the high impact rare event.