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Incorporating higher moments into value-at-risk forecasting

Author

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  • Arnold Polanski

    (Queen's University Management School, Belfast, UK)

  • Evarist Stoja

    (School of Economics, Finance and Management, University of Bristol, UK)

Abstract

Value-at-risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time-varying higher-moments models. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Arnold Polanski & Evarist Stoja, 2010. "Incorporating higher moments into value-at-risk forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(6), pages 523-535.
    • Handle: RePEc:jof:jforec:v:29:y:2010:i:6:p:523-535
    DOI: 10.1002/for.1155
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    References listed on IDEAS

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    6. Huang, Zhuo & Liang, Fang & Wang, Tianyi & Li, Chao, 2021. "Modeling dynamic higher moments of crude oil futures," Finance Research Letters, Elsevier, vol. 39(C).
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    11. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2017. "Risk quantification in turmoil markets," Risk Management, Palgrave Macmillan, vol. 19(3), pages 202-224, August.
    12. León, Ángel & Ñíguez, Trino-Manuel, 2021. "The transformed Gram Charlier distribution: Parametric properties and financial risk applications," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 323-349.
    13. Wang, Tianyi & Liang, Fang & Huang, Zhuo & Yan, Hong, 2022. "Do realized higher moments have information content? - VaR forecasting based on the realized GARCH-RSRK model," Economic Modelling, Elsevier, vol. 109(C).
    14. Andrés Mora-Valencia & Trino-Manuel Ñíguez & Javier Perote, 2017. "Multivariate approximations to portfolio return distribution," Computational and Mathematical Organization Theory, Springer, vol. 23(3), pages 347-361, September.
    15. Mateusz Buczyński & Marcin Chlebus, . "Old-fashioned parametric models are still the best: a comparison of value-at-risk approaches in several volatility states," Journal of Risk Model Validation, Journal of Risk Model Validation.
    16. Yanwei Jia & Jussi Keppo & Ville Satopää, 2023. "Herding in Probabilistic Forecasts," Management Science, INFORMS, vol. 69(5), pages 2713-2732, May.
    17. Abad, Pilar & Benito, Sonia, 2013. "A detailed comparison of value at risk estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 258-276.
    18. Olivier Bos & Béatrice Roussillon & Paul Schweinzer, 2016. "Agreeing on Efficient Emissions Reduction," Scandinavian Journal of Economics, Wiley Blackwell, vol. 118(4), pages 785-815, October.
    19. Sonia Benito Muela & Carmen López-Martín & Mª Ángeles Navarro, 2017. "The Role of the Skewed Distributions in the Framework of Extreme Value Theory (EVT)," International Business Research, Canadian Center of Science and Education, vol. 10(11), pages 88-102, November.
    20. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 531-537.
    21. Cui, Jinxin & Maghyereh, Aktham & Liao, Dijia, 2024. "Risk connectedness between international oil and stock markets during the COVID-19 pandemic and the Russia-Ukraine conflict: Fresh evidence from the higher-order moments," International Review of Economics & Finance, Elsevier, vol. 95(C).
    22. Pilar Abad Romero & Sonia Benito Muela & Miguel Angel Sánchez Granero & Carmen López, 2013. "Evaluating the performance of the skewed distributions to forecast Value at Risk in the Global Financial Crisis," Documentos de Trabajo del ICAE 2013-40, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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