On the methodologies of threshold selection in the context of Peaks Over Threshold approach for market risk modelling Cordero Romero, Juan Francisco * Benito Muela, Sonia † December 7, 2023 Abstract The Peaks Over Threshold (POT) model has emerged as a highly promising approach for estimating crucial market risk metrics like Expected Shortfall and Value at Risk. Nonetheless, this technique presents a major challenge: there is not a standard methodology to choose the optimal threshold that separates extreme values of an empirical distribution from the rest. As a result, several approaches for the determination of this threshold have been developed in the last years. In this context, this study aims to conduct a comprehensive comparative analysis of various optimal threshold selection methodologies within the Peak Over Threshold framework, as applied to the measurement of market risk. The primary objective is to examine the influence of these methodologies on market risk assessments and capital requirement calculations. With this goal, we analyze the results in terms of threshold return values, market risk measures and daily capital requirements for eight different methodologies of threshold selection. We conclude that, even though considerable discrepancies can be observed between methodologies in terms of threshold returns values, these discrepancies do not translate into large deviations in terms of market risk measurements and capital requirements estimates. Consequently, the selection of the optimal threshold selection methodology may not wield substantial relevance in determining the eventual outcomes. Keywords: Extreme Value Theory, Value at Risk, Peaks Over Threshold. 1 Introduccion Extreme Value Theory (EVT), also referred to as Extreme Value Analysis (EVA) is a branch of statistics that focuses on limiting the distribution of extreme returns observed over a long period, which is independent of the distribution of the returns themselves. Therefore, EVT is especially relevant in areas where extreme events are of interest. Its applications are vast and highly heterogeneous. Some of the most notable research fields in which the application of Extreme Value Analysis takes place are engineering, climatology, and seismology, among others. For instance, in the discipline of coastal engineering, Li et al. (2014) make use of Extreme Value Theory to model the probability of severe storms along the Dutch coast. Similarly, in the area of engineering hydrology and climatology, Beguer´ ıa and Vicente-Serrano (2006) models the probability of extreme rainfalls in the middle Ebro Valley (Spain) through a procedure based on extreme value analysis and spatial interpolation techniques. In this same area, Overeem et al. (2010) propose a method to * Contact: corderjuan13@gmail.com † Contact: soniabm@cee.uned.es 1