Assessing the performance of the Block Maxima Method in estimating market risk

Extreme value theory has been widely used in many fields, such as engineering, insurance, meteorology, and more recently finance. In this last area, the POT method has yielded very good results, especially in quantifying market risk. The performance of the BMM in this field has been scarcely studied. Thus, the study conducted in this paper contributes to the literature in three aspects. First, it analyses the performance of the BMM in estimating market risk. As we have said before, few studies have analyzed this issue. Second, we assess to what extent the selection of the block size is significant in quantifying market risk. Finally, a third contribution emerges from this work by comparing the performance of the BMM with that of the POT method in estimating market risk.For this study, daily data from January 3rd, 2000, to December 31st, 2019, were used for the S&P 500 returns. To quantify market risk, two measures have been considered: Value at Risk (VaR) and Expected Shortfall (ES). For calculating risk, two confidence levels were used: 97.5% and 99%. To apply the BMM, nine different block sizes were considered: 5, 10, 21, 31, 42, 63, 126, 189 and 252 observations.The results obtained are as follows. First, we detect that the VaR estimations are highly sensitive to the block size selected for fitting the GEV distribution. Both the lowest block size and the higher block size provide inaccurate market risk estimations. Only the intermediate block size provides reasonable VaR estimations. Second, in the case of Expected Shortfall, we found a strong risk overestimation for all the block sizes analyzed.To corroborate these results, we have extended the S&P 500 index study to a set of 14 assets (stock market indexes, commodities, and rate exchanges). The results go in the same direction, indicating that the Block Maxima Method does not provide appropriate market risk estimations and fundamentally depends on the block size selected. Only the intermediate block size seems to perform well, although the results are not robust, in the sense that no one block size performs well for all assets considered.Finally, a comparison of the VaR estimates obtained under the POT method and the BMM is conducted. According to the percentage of exceptions reaped by each method, the POT method clearly outperforms the BMM, as the former provides a more accurate VaR estimate and is more consistent, as the results do not depend on the threshold choice.