How accurate are modern Value-at-Risk estimators derived from extreme value theory?

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. In this study, we compare the out-of-sample forecasting performance of several modern Valueat-Risk (VaR) estimators derived from extreme value theory (EVT). Specifically, in a multiasset study covering 30 years of stock, bond, commodity and currency market data, we analyse the accuracy of the classic generalised Pareto peak over threshold approach and three recently proposed methods based on the Box-Cox transformation, L-moment estimation and the Johnson system of distributions. We find that, in their unconditional form, some of the estimators are acceptable under current regulatory assessment rules but none of them can continuously pass more advanced tests of forecasting accuracy. In their conditional forms, forecasting power is significantly increased and the Box-Cox method proves to be the most promising estimator. However, it is also important to stress that the traditional historical simulation approach, which is currently the most frequently used VaR estimator in commercial banks, can not only keep up with the EVT-based methods but occasionally even outperforms them (depending on the setting: unconditional vs. conditional). Thus, recent claims to generally replace this simple method by theoretically more advanced EVT-based methods may be premature. Terms of use: Documents inJEL-Codes: G100, G110, G170.

Time‐varying dynamics of expected shortfall in commodity futures markets

“…Additional distributions, based on and generalizing normal transformations, are contained in the distribution system of Johnson (1949), which has been compared in detail to the ‐and‐ distribution in Mac Gillivray (1992) and applied by Mögel and Auer (2018) to model the VaR of London Bullion Market gold spot returns. In this system, the associated cdf for is where and determine the shape of the distribution, is a location, and a scale factor.…”

A Monte Carlo evaluation of non-parametric estimators of expected shortfall

“…Because the ES focuses on extreme losses, extreme value theory is a particularly interesting tool for the derivation of new ES estimators. So far, most research in this field has focused on VaR estimation (Brooks et al , 2005; Mögel and Auer, 2018) but can easily be extended to ES estimation (McNeil and Frey, 2000; Martins-Filho and Yao, 2006; Martins-Filho et al , 2018). Motivated by its popularity and persuasive backtest performance for high confidence levels (Gençay and Selçuk, 2004), we let the peak-over-threshold (POT) method represent the class of estimators based on extreme value theory.…”

Investment Environment Problems Analysis and Evaluation: An Ex Post Empirical Analysis and Performance Implications

“…The implementation of the VaR models and their performance were considered by many authors, both from the theoretical and practical point of view (Kang & Li, 2018;Mogel & Auer, 2018;Trottier et al, 2018;Bee et al, 2017;D'Amico & Petroni, 2017;Djakovic & Andjelic, 2017;Goel et al, 2017;Chen & Chiang, 2016;Kambouroudis et al, 2016;Lee, 2016;Wied et al, 2016;Zhou et al, 2016). The evolution of risk management is induced by financial crises (Adrian, 2017).…”