Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance

This paper conducts a comparative evaluation of the predictive performance of various Value-at- Risk (VaR) models. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): the Peaks over Threshold (POT) and the Blocks Maxima (BM). Both estimation techniques are based on limit results for the excess distribution over high thresholds and block maxima, respectively. They are applied on, USD-denominated, daily returns of the Dow Jones Industrial Average (DJIA) and the Cyprus Stock Exchange (CSE) indices with the intension to compare the performance of the various estimation techniques on markets with different capitalization and trading practices. The sample extends over the period November 21, 1997 to April 19, 2002 while the sub-period April 12, 2001 to April 19, 2002 has been reserved for backtesting purposes. The results we report reinforce previous ones according to which at very high confidence levels the EVT-based methodology produces the most accurate forecasts of extreme losses.