Predictive performance of conditional Extreme Value Theory in Value-at-Risk estimation

Abstract

This paper conducts a comparative evaluation of the predictive performance of various Value-at-Risk (VaR) models. Special emphasis is paid to two methodologies related to the Extreme Value Theory (EVT): The Peaks Over Threshold (POT) and the Block Maxima (BM). We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the BVMT and CAC 40 indices with the intention to compare the performance of various estimation methods on markets with different capitalisation and trading practices. The results we report demonstrate that conditional POT EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate.