Financial Risk Modelling and Portfolio Optimization with R

7

Extreme value theory

7.1 Preliminaries

Extreme value theory (EVT) is a branch of statistics. Its subject is the modelling of large deviations from the median of a distribution. EVT is by no means a young discipline – its roots can be traced back to the 1920s. However, interest in EVT and its application to modelling financial market risks has picked up only during the last decade among practitioners. The reason for this development might well be the increasing occurrence of financial market turmoil episodes.

This chapter begins with the theoretical underpinnings of EVT. Three approaches to modelling extreme values are presented: the block maxima method, the peaks-over-threshold method and Poisson processes. This exposition is by no means exhaustive, and its purpose is only to help the reader gain a better idea of how these methods are implemented in . For a more thorough treatment of the subject the reader is referred to the monographs of Coles (2001), Embrechts et al. (1997), Leadbetter et al. (1983) and McNeil et al. (2005, Chapter 7).

Section 7.3 provides a synopsis of the currently available packages in . Although there is quite an overlap between the various EVT models and their implementations in , a comparison of the various packages reveals subtle differences, weaknesses ...