The problem posed by this estimator is the lack of any analytical means to choose the threshold value of u in an optimum manner. Hence, as an alternative, the procedure involves using the feature known as Hill graphics. Different values of the Hill index are calculated for different u values; the Hill estimator values become represented in a chart or graphic based on u, and the u value is selected from the region where the Hill estimators are relatively stable (Hill chart leaning almost horizontally). The underlying intuitive idea posed in the Hill chart is that as u increases, the estimator variance decreases, and thus, the bias is increased. Therefore, the ability to foresee a balance between both trends is likely. When this level is reached, the estimator remains constant.
Existing literature on EVT models to calculate VaR is abundant. Regarding BMM, Silva and Melo (2003) considered different maximum block widths, with results suggesting that the extreme value method of estimating the VaR is a more conservative approach for determining the capital requirements than traditional methods. Byström (2004) applied both unconditional and conditional EVT models to the management of extreme market risks in the stock market and found that conditional EVT models provided particularly accurate VaR measures. In addition, a comparison with traditional Parametric (GARCH) approaches to calculate the VaR demonstrated EVT as being the superior approach for both standard and more extreme VaR quantiles. Bekiros and Georgoutsos (2005) conducted a comparative evaluation of the predictive performance of various VaR models, with a special emphasis on two methodologies related to the EVT, POT and BM. Their results reinforced previous results and demonstrated that some “traditional” methods might yield similar results at conventional confidence levels but that the EVT methodology produces the most accurate forecasts of extreme losses at very high confidence levels. Tolikas et al. (2007) compared EVT with traditional measures (Parametric method, HS and Monte Carlo) and agreed with Bekiros and Georgoutsos (2005) on the outperformance of the EVT methods compared with the rest, especially at very high confidence levels. The only model that had a performance comparable with that of the EVT is the HS model.