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


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


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, Skewnessn and Kurtosis in an Exponential Weighted Moving Average Framework," Working Papers wp831, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:wp831

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    References listed on IDEAS

    1. Marcucci Juri, 2005. "Forecasting Stock Market Volatility with Regime-Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-55, December.
    2. Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.
    3. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    4. Aamir R. Hashmi & Anthony S. Tay, 2001. "Global and Regional Sources of Risk in Equity Markets: Evidence from Factor Models with Time-Varying Conditional Skewness," Departmental Working Papers wp0116, National University of Singapore, Department of Economics.
    5. Anders Wilhelmsson, 2009. "Value at Risk with time varying variance, skewness and kurtosis--the NIG-ACD model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 82-104, March.
    6. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    7. 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.
    8. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2007. "A robust VaR model under different time periods and weighting schemes," Review of Quantitative Finance and Accounting, Springer, vol. 28(2), pages 187-201, February.
    9. Esther B. Del Brio & Trino-Manuel Niguez & Javier Perote, 2009. "Gram-Charlier densities: a multivariate approach," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 855-868.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    12. Alizadeh, Amir H. & Gabrielsen, Alexandros, 2013. "Dynamics of credit spread moments of European corporate bond indexes," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3125-3144.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.

    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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