Abstract

This chapter is dedicated to tail (or extreme) risk modeling. Tail risk recovers two notions. The first one is related to rare events, meaning that a severe loss may occur with a very small probability. The second one concerns the magnitude of a loss that is difficult to reconciliate with the observed volatility of the portfolio. Of course, the two notions are connected, but the second is more frequent. For instance, stock market crashes are numerous since the end of the eighties. The study of these rare or abnormal events needs an appropriate framework to analyze their risk. This is the subject of this chapter. In a first section, we consider order statistics, which are very useful to understand the underlying concept of tail risk. Then, we present the extreme value theory (EVT) in the unidimensional case. Finally, the last section deals with the correlation issue between extreme risks.