To continue my story of yesterday, here is the development of the DAX.
It shows, by the way, that the current fuzz about dropping stock rates is somewhat exaggerated. The DAX is still higher than 2003. The plot also shows that stock markets got crazy around 1998. Probably, because people got crazy.
Now, I like to study the deltas. Here is a plot of the deltas (scaled to delta per day). The function is the corresponding Gauß distribution, which does obviously not fit very well. There are too little intermediate deltas.
Instead, we look at the excessive deltas (in absolute value). And indeed, we find a power law.
The plot shows excess(x)*x^3.6, where excess(x) is the number of deltas larger than x*var in absolute value (var is the observed variance of the deltas).
So we can explain the excessive deltas by the power law with exponent 3.6, just as claimed by Taleb.