Next Article in Journal
Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology
Previous Article in Journal
Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications
Open AccessArticle

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

Department of Operations Research, Poznań University of Economics and Business, Al. Niepodległości 10, 61-875 Poznań, Poland
Department of Finance and Accounting, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland
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;
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
Show Figures

Figure 1

MDPI and ACS Style

Echaust, K.; Just, M. Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection. Mathematics 2020, 8, 114.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop