Returns of various financial assets are analysed using the techniques of Extreme Value Theory and using fat-tailed distributions using R in Jupyter Notebook. Here I also post the pictures which could not be rendered properly in the notebook.
Apple excess distribution and the fitted power law
The excess distribution seems to fit the data nicely.
Apple survival function and the fitted power law
The tail is also fitted nicely. Notice that now we are able to capture the observation in the very tail (corresponding to the loss of 20%)
Residuals of the fit of power law to Apple lossess
The residuals in the scatterplot seem to be pretty random and don't show any pattern which is a sign of a good fit.
QQ-plot of the residuals
They are pretty well fitted to the thin-tailed exponential distribution which means that we were able to explain much of the "fattness of the tail"