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Open AccessArticle

On the Statistical GARCH Model for Managing the Risk by Employing a Fat-Tailed Distribution in Finance

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Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
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Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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AMPSAS, University College Dublin, 4 Dublin, Ireland
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1698; https://doi.org/10.3390/sym12101698
Received: 7 September 2020 / Revised: 8 October 2020 / Accepted: 10 October 2020 / Published: 15 October 2020
The Conditional Value-at-Risk (CVaR) is a coherent measure that evaluates the risk for different investing scenarios. On the other hand, since the extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, we here employ this distribution in investigating explicit formulas for the two common risk measures, i.e., VaR and CVaR, to have better tools in risk management. The formulas are then employed under the generalized autoregressive conditional heteroskedasticity (GARCH) model for risk management as our main contribution. To confirm the theoretical discussions of this work, the daily returns of several stocks are considered and worked out. The simulation results uphold the superiority of our findings. View Full-Text
Keywords: conditional value-at-risk; GARCH model; CVaR; extreme value distribution; risk allocation conditional value-at-risk; GARCH model; CVaR; extreme value distribution; risk allocation
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Long, H.V.; Jebreen, H.B.; Dassios, I.; Baleanu, D. On the Statistical GARCH Model for Managing the Risk by Employing a Fat-Tailed Distribution in Finance. Symmetry 2020, 12, 1698.

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