Extreme Value Theory for Finance: A Survey

Extreme value theory is concerned with the study of the asymptotical distribution of extreme events, that is to say events which are rare in frequency and huge with respect to the majority of observations. Statistical methods derived from this theory have been increasingly employed in nance, especially in the context of risk measurement. The aim of the present study is two-fold. The rst part delivers a critical review of the theoretical underpinnings of extreme value theory. The second part provides a survey of some major applications of extreme value theory to nance, namely its use to test between different distributional assumptions for the data, Value-at-Risk and Expected Shortfall calculations, asset allocation under safety- rst type constraints and the study of contagion and dependence across markets under stress conditions.