I started researching this topic and it is well covered in the literature. My understanding is that it uses a historical time series of returns of a given set of stocks and represent such distributions by a combination of a Gaussian kernel and a generalized Pareto distribution (GPD) for the tails. This approach requires a filtering of the returns data via GARCH or ARIMA methods, which is apparently necessary to remove heteroskedasticity and other “bad” properties (non IID) that are otherwise out of the scope with the theory of EVT. I think these transformations must subsequently be undone to obtain “real” simulated returns. Lastly, to correlate the simulated variables, a T or elliptical copula can then be used on the individual CDFs calibrated as above. A more “naive” approach would be to simply use empirical CDF from each stock return series, and also apply a copula to generate correlated returns. So what is the value of the more complex EVT approach? I assume the main reason is that with historical, you cannot generate extreme returns that are lower(greater) than the minimum(maximum) of the historical returns for each stock. Whereas the parameters of the GPD can obviously be tweaked to produce more extremes, but how unrealistic can it become? I saw a short paper from Taleb where he shows that the impact on these methods can be (pun intended) extreme and impractical to use. So I am wondering what the main advantages are of implementing a somehow complex approach such as this?