On the Conditional Value at Risk Based on the Laplace Distribution with Application in GARCH Model

Malik Zaka Ullah, Fouad Othman Mallawi, Mir Asma and Stanford Shateyi ()
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Malik Zaka Ullah: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Fouad Othman Mallawi: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Mir Asma: Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2022, vol. 10, issue 16, 1-13

Abstract: In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock movement by using the GARCH model. Numerical simulations are given for a variety of stocks in equity markets to uphold the findings.

Keywords: risk measure; stock market; Laplace distribution; non-normality; fat-tail (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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