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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Malik Zaka Ullah & Fouad Othman Mallawi & Mir Asma & Stanford Shateyi, 2022. "On the Conditional Value at Risk Based on the Laplace Distribution with Application in GARCH Model," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3018-:d:894242
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    References listed on IDEAS

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    1. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2021. "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation," Annals of Operations Research, Springer, vol. 299(1), pages 1281-1315, April.
    2. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    3. Manuela Braione & Nicolas K. Scholtes, 2016. "Forecasting Value-at-Risk under Different Distributional Assumptions," Econometrics, MDPI, vol. 4(1), pages 1-27, January.
    4. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Ahmed, Dilan & Soleymani, Fazlollah & Ullah, Malik Zaka & Hasan, Hataw, 2021. "Managing the risk based on entropic value-at-risk under a normal-Rayleigh distribution," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    7. Wang, Gang-Jin & Zhu, Chun-Long, 2021. "BP-CVaR: A novel model of estimating CVaR with back propagation algorithm," Economics Letters, Elsevier, vol. 209(C).
    8. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    9. Bormetti, Giacomo & Cisana, Enrica & Montagna, Guido & Nicrosini, Oreste, 2007. "A non-Gaussian approach to risk measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 532-542.
    10. BRAIONE, Manuela & SCHOLTES, Nicolas K., 2016. "Forecasting Value-at-Risk under Different Distributional Assumptions," LIDAM Reprints CORE 2733, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Value-at-risk methodologies for effective energy portfolio risk management," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 197-212.
    12. Nicholas L. Georgakopoulos, 2018. "Illustrating Finance Policy with Mathematica," Quantitative Perspectives on Behavioral Economics and Finance, Palgrave Macmillan, number 978-3-319-95372-4, February.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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