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Open AccessArticle

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

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Department of Operations Research, Poznań University of Economics and Business, Al. Niepodległości 10, 61-875 Poznań, Poland
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Department of Finance and Accounting, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland
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Author to whom correspondence should be addressed.
This paper is an extended version of the paper published in the Proceedings of 10th Economics & Finance Conference, Rome, Italy, 10 September 2018.
Mathematics 2020, 8(1), 114; https://doi.org/10.3390/math8010114
Received: 25 November 2019 / Revised: 30 December 2019 / Accepted: 9 January 2020 / Published: 11 January 2020
(This article belongs to the Special Issue Computational Statistical Methods and Extreme Value Theory)
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. View Full-Text
Keywords: Value at Risk; optimal tail selection; Extreme Value Theory; GARCH-EVT Value at Risk; optimal tail selection; Extreme Value Theory; GARCH-EVT
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Echaust, K.; Just, M. Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection. Mathematics 2020, 8, 114.

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