A scientific way of looking beyond the worst-case return is to employ statistical
extreme value methods. Extreme Value Theory (EVT) shows that the probability on
very large losses is eventually governed by a simple function, regardless the specific
distribution that underlies the return process. This limit result can be exploited to
construct semi-parametric portfolio Value at Risk (VaR) estimates around and beyond
the largest observed loss. Such extreme VaR estimates can be useful inputs for
scenario analysis and stress testing. The aim of this chapter is to introduce the reader
to extreme value theory and the statistics of extremes