Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection

Krzysztof Echaust , Małgorzata Just

Abstract

A conditional Extreme Value Theory (GARCH-EVT) approach is a two-stage hybrid method that combines a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) filter with the Extreme Value Theory (EVT). The approach requires pre-specification of a threshold separating distribution tails from its middle part. The appropriate choice of a threshold level is a demanding task. In this paper we use four different optimal tail selection algorithms, i.e., the path stability method, the automated Eye-Ball method, the minimization of asymptotic mean squared error method and the distance metric method with a mean absolute penalty function, to estimate out-of-sample Value at Risk (VaR) forecasts and compare them to the fixed threshold approach. Unlike other studies, we update the optimal fraction of the tail for each rolling window of the returns. The research objective is to verify to what extent optimization procedures can improve VaR estimates compared to the fixed threshold approach. Results are presented for a long and a short position applying 10 world stock indices in the period from 2000 to June 2019. Although each approach generates different threshold levels, the GARCH-EVT model produces similar Value at Risk estimates. Therefore, no improvement of VaR accuracy may be observed relative to the conservative approach taking the 95th quantile of returns as a threshold.
Author Krzysztof Echaust (WIiGE / KBO)
Krzysztof Echaust,,
- Department of Operations Research
, Małgorzata Just - Uniwersytet Przyrodniczy w Poznaniu, MNiSW [80]
Małgorzata Just,,
-
Journal seriesMathematics, ISSN 2227-7390, (N/A 20 pkt)
Issue year2020
Vol8
No1
Pages1-24
Publication size in sheets1.15
Article number114
Keywords in PolishValue at Risk; optymalny wybór ogona rozkładu; teoria wartości ekstremalnych; GARCH-EVT
Keywords in EnglishValue at Risk; optimal tail selection; Extreme Value Theory; GARCH-EVT
DOIDOI:10.3390/math8010114
URL https://www.mdpi.com/2227-7390/8/1/114
Languageen angielski
Score (nominal)20
Score sourcejournalList
ScoreMinisterial score = 20.0, 18-02-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; WoS Impact Factor: 2018 = 1.105 (2)
Citation count*1 (2020-06-29)
Additional fields
UwagiSpecial Issue: Computational Statistical Methods and Extreme Value Theory
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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