It's to do with the asian and russian crises of the late 90s, which he felt showed that the black-scholes models were wrong and inferior to his own multifractal view of the market. After those crashes, he wrote articles and books attacking those ideas.
When you model equities as log-normal ie. log(stock price) is normally distributed, and then use the geometric brownian motion to model the underlying, which spits out derivative prices using Black-Scholes.
The problem is that normal distribution is thin-tailed ie. 5 sigma events are extremely rare.
So use a fat tailed distribution - which is what Mandelbrot did. He used a power-law ( Pareto ) distribution because its infinite variance permitted wider swings in price than the Gaussian. However the simplicity of using a Normal distribution is what makes Black Scholes so robust. If a thousand statisticians look at market data over a time window & model it to fit a lognormal usaing MLE, they'll come up with approximately the same parameters, so calibration is relatively easy. In fact this is one of the standard exercises in any MFE pgm - to calibrate a derivatives model corresponding to underlying data over a time window.
With Mandelbrot's Paretian distribution, calibration is virtually impossible. No two people get the same parameters given the same data points on a Paretian model. There is quite a bit of literature on this very topic, in both Taleb's last book & elsewhere. Mandelbrot points out how given different time windows, the Paretian distribution can be calibrated to fit virtually anything, but the parameters will change wildly.
Essentially, given the choice between an inaccurate robust simple Gaussian model with high predictive power and a supposedly accurate but un-usable Paretian model, financial engineers choose the former & add fudge-factor explanations ( eg. the vol-smile ) to augment the data.
Every trader knows black-scholes doesn't work. According to black-scholes the volatility curve should be flat, but it is actually a smile. Believing black-scholes works is like believing the earth is flat.
BS is one of the most robust computationally amenable closed-form pricers out there.
What does that mean ?
1. Closed-form computationally amenable:
Most pricers aren't closed form. They require you to evaluate an integral using finite differences or a million montecarlo simulations to trace out paths over a binomial tree. MC introduces huge variance so you need antithetic methods & control variates to damp.
http://en.wikipedia.org/wiki/Antithetic_variates
BS is a simple closed form formula that has been programmed in over 30 languages in like 10 lines of code ( Objective-C/iPhone, F#, Autoit, Fortress, Lua, APL, SAS, Mathcad, J, MEL, Postscript, VB.NET, Clean, Ruby, Lisp, Prolog, PL/SQL, LyME, ColdFusion, K, C#, HP48, Transact SQL, O'Caml, Rebol, Real Basic, Icon, Squeak, Haskell, JAVA , JavaScript, VBA, C++, Perl, Maple, Mathematica, Matlab, S-Plus, IDL, Pascal, Python, Fortran, Scheme, PHP, GNU, gnuplot )
2. Incredibly robust:
BS requires very few free params to spit out a ballpark price. That ballpark price is remarkably accurate.
eg. A 3 month at-the-money call should cost
"one-fifth spot times vol. " ( they make us memorize this in class :)
That's it! That's a frequently used Black-Scholes approx.
So call price = S times sigma/5.
So a Cisco September $15 call should be about
15 times 30%/5 = 90 cents.
Guess how much its trading at right now ?
That's right, 88 cents!
See for yourself: http://finance.yahoo.com/q/op?s=CSCO&m=2011-09
Can't get any more robust than that.
It is remarkably accurate ATM, and there are well-known fudge-factors & rules of thumb you can employ as you go deep ITM or deep OTM.
"According to black-scholes the volatility curve should be flat, but it is actually a smile"
Ummm...BS doesn't say anything about a vol curve. It says vol is a single param. A const. A final. So BS assumes vol is constant at all maturities. If you plot a vol curve by graphing vol vs maturities, you will obviously get different shapes in practice. Sometimes you get a smile ( bonds ), other times a skew ( stocks ), other times other weird shapes. Essentially the shape says people prefer ATM options to deep ITM or deep OTM, but obviously prices are dictated by supply-demand, not by some model. So BS is mispricing OTMs & ITMs, but to imply "BS says vol curve should be flat but its not really flat" is backwards. BS assumed vol to be a fixed single param, and any model that assumes vol to change ( say Heston's stochastic local vol ) over maturities will have a really tough time calibrating params for that model. Heston itself requires 5 params...not easy to calibrate.
http://en.wikipedia.org/wiki/Stochastic_volatility
"Believing black-scholes works is like believing the earth is flat."
No its not. 1000 times not.
Believing black-scholes is like believing the earth is a sphere. Is the earth a sphere ? No, its a geoid. ( http://en.wikipedia.org/wiki/Reference_ellipsoid )
But is a sphere a good ballpark approx ? Yeah, a very good one, in fact. Well then, so is BS.
Guess what Benoît Mandelbrot studied before he started doing pure maths? ;)
EDIT: for bonus points, guess why he fell out with his old friends in the 90s.