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Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework

Author

Listed:
  • A. Gabrielsen
  • P. Zagaglia
  • A. Kirchner
  • Z. Liu

Abstract

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and kurtosis appear directly in the functional form of this density. In this setting VaR can be described as a function of the time-varying higher moments by applying the Cornish-Fisher expansion series of the first four moments. An evaluation of the predictive performance of the proposed model in the estimation of 1-day and 10-day VaR forecasts is performed in comparison with the historical simulation, filtered historical simulation and GARCH model. The adequacy of the VaR forecasts is evaluated under the unconditional, independence and conditional likelihood ratio tests as well as Basel II regulatory tests. The results presented have significant implications for risk management, trading and hedging activities as well as in the pricing of equity derivatives.

Suggested Citation

  • A. Gabrielsen & P. Zagaglia & A. Kirchner & Z. Liu, 2012. "Forecasting Value-at-Risk with Time-Varying Variance, Skewness and Kurtosis in an Exponential Weighted Moving Average Framework," Papers 1206.1380, arXiv.org.
    • Handle: RePEc:arx:papers:1206.1380
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    Cited by:

    1. Ji Cao, 2017. "How does the underlying affect the risk-return profiles of structured products?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(1), pages 27-47, February.
    2. Lucas, André & Zhang, Xin, 2016. "Score-driven exponentially weighted moving averages and Value-at-Risk forecasting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 293-302.
    3. Huang, Zhuo & Liang, Fang & Wang, Tianyi & Li, Chao, 2021. "Modeling dynamic higher moments of crude oil futures," Finance Research Letters, Elsevier, vol. 39(C).
    4. Kim-Hung Pho & Ngoc-Hien Nguyen & Huu-Nhan Huynh & Wing-Keung Wong, 2021. "A Detailed Guide on How to Use Statistical Software R for Text Mining," Advances in Decision Sciences, Asia University, Taiwan, vol. 25(3), pages 92-110, September.
    5. 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.
    6. Wentao Hu, 2019. "calculation worst-case Value-at-Risk prediction using empirical data under model uncertainty," Papers 1908.00982, arXiv.org.
    7. Radu Lupu, 2014. "Simultaneity of Tail Events for Dynamic Conditional Distributions of Stock Market Index Returns," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 49-64, December.
    8. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    9. Zoran Ivanovski & Zoran Narasanov & Nadica Ivanovska, 2015. "Volatility And Kurtosis At Emerging Markets: Comparative Analysis Of Macedonian Stock Exchange And Six Stock Markets From Central And Eastern Europe," Economy & Business Journal, International Scientific Publications, Bulgaria, vol. 9(1), pages 84-93.
    10. Ivanovski, Zoran & Stojanovski, Toni & Narasanov, Zoran, 2015. "Volatility And Kurtosis Of Daily Stock Returns At Mse," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 6(2), pages 209-221.
    11. Massimiliano Frezza & Sergio Bianchi & Augusto Pianese, 2022. "Forecasting Value-at-Risk in turbulent stock markets via the local regularity of the price process," Computational Management Science, Springer, vol. 19(1), pages 99-132, January.

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    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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