Extreme value theory and statistics for heavy tail data

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.