1) 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) 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 by using put-call parity.
3) Option traders did not use formulas after 1973 but continued their bottom-up heuristics.
The Bachelier-Thorp approach is more robust (among other things) to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop calling the formula by the wrong name."
An excellent summation of Taleb's critique is "Whither Black-Scholes?""
Although one might temper one's judgement by reading "Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments"
by Justin Kruger and David Dunning of Cornell University"
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075
from the abstract:
"we have historical evidence that
1) 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) 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 by using put-call parity.
3) Option traders did not use formulas after 1973 but continued their bottom-up heuristics.
The Bachelier-Thorp approach is more robust (among other things) to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop calling the formula by the wrong name."
An excellent summation of Taleb's critique is "Whither Black-Scholes?""
http://www.forbes.com/2008/04/07/black-scholes-options-oped-...