Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT)

Abstract

From a theoretical point of view, the selection of thresholds is a critical issue in the framework of the Peaks Over Threshold (POT) approach, which is why in the last decade numerous methodologies have been proposed for its selection. In this paper, we address this subject from an empirical point of view by assessing to what extent the selection of the threshold is decisive in quantifying the market risk. For measuring market risk, we use the Value at Risk (VaR) and the Expected Shortfall (ES) measures. The results obtained indicate that there is a large set of thresholds that provide similar Generalized Pareto Distribution (GPD) quantiles estimators and as a consequence similar market risk measures. Just only, for large thresholds, those corresponding to the 98th and 99th percentile of the GPD some differences are found. It means that the choice of threshold in the framework of the POT method may not be relevant in quantifying market risk when we use the VaR and ES measures for this task.

Assessing the Performance of the Block Maxima Method in Estimating Market Risk

“…Furthermore, the performance of this method is independent of the choice of threshold, at least within the range considered in this study. This last result corroborates the results obtained by Benito et al (2023), who indicate that in the context of the POT method, the threshold choice may not be relevant in quantifying market risk. The results reported in this section provide additional evidence regarding the superiority of the POT method over the BBM in estimating market risk.…”

“…where 𝑢 represents the threshold choice; 𝜎 and 𝜉 are the scale and shape parameters, respectively, of the GPD; 𝑛 is the size of the sample; and 𝑁 𝑢 is the number of data points over the threshold choice; see Benito et al (2023) for a detailed review of this method.…”

“…In the same vein as in the study conducted by Benito et al (2023), in this article, we analyze whether the selection of the block size significantly influences the measurement of market risk. Following these authors, the risk measures used in this analysis are the value at risk (VaR) measure and the expected shortfall (ES) measure.…”

“…The extreme value theory is well established in many fields, such as civil engineering (Wu and Qiu, 2018), climatology (Davison and Smith, 1990; Kharin et al 2013), seismology (Beirlant et al 2018) and hydrology (Katz et al 2002, Carreau et al 2017, Bader et al 2018). As Benito et al (2023) remarked, in the field of civil engineering, EVT can be used in bridge design and risk assessment. In seismology and climatology, extreme value analysis is used to study earthquakes and extreme precipitation, while in hydrology, extreme value analysis is a valuable tool for studying coastal flood risk.…”

“…Although the selection of these variables seems crucial from a theoretical point of view, a recent empirical study has shown that in the context of the POT method, the selection of the threshold is not relevant in quantifying market risk (Benito et al, 2023). These authors showed that there is a large set of thresholds between the threshold corresponding to the 85 th to the 95 th percentile that provide the same market risk estimations; therefore, in this range, the choice of threshold may be irrelevant in the cited field.…”