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.

1. http://blogs.reuters.com/justinfox/2010/10/18/why-didn%E2%80... 2. http://en.wikipedia.org/wiki/Fat_tail 3. http://brokensymmetry.typepad.com/broken_symmetry/2009/08/wh...