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Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence


  • ROCKINGER, Michael
  • JONDEAU, Eric


Recent portfolio choice, asset pricing, and option valuation models highlight the importance of skewness and kurtosis. Since skewness and kurtosis are related to extreme variations, they are also important for Value-at-Risk measurements. Our framework builds on a GARCH model with a conditional generalized-t distribution for residuals. We compute the skewness and kurtosis for this model and compare the range of these moments with the maximal theoretical moments. Our model, thus allows for time-varying conditional skewness and kurtosis. We implement the model as a constrained optimization with possibly several thousand restrictions on the dynamics. A sequential quadratic programming algorithm successfully estimates all the models, on a PC, within at most 50 seconds. Estimators, obtained with logistically-constrained dynamics, have different properties. We apply this model to daily and weekly foreign exchange returns, stock returns, and interest-rate changes. This finding is consistent with findings from extreme value theory. Kurtosis exists on fewer dates and for fewer series. There is little evidence, at the weekly frequency, of time-variability of conditional higher moments. Transition matrices document that agitated stares come as a surprise and that there is a certain persistence in moments beyond volatility. For exchange-rate and stock-market data, cross-sectionally and at daily frequency, we also document co-variability of moments beyond volatility.

Suggested Citation

  • ROCKINGER, Michael & JONDEAU, Eric, 2000. "Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence," Les Cahiers de Recherche 710, HEC Paris.
  • Handle: RePEc:ebg:heccah:0710

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    Cited by:

    1. 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.
    2. Rockinger, M. & Jondeau, E., 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working papers 82, Banque de France.
    3. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
    4. Ibrahim Onour, "undated". "Exploring Stability of Systematic Risk: Sectoral Portfolio Analysis," API-Working Paper Series 1002, Arab Planning Institute - Kuwait, Information Center.
    5. Tao Pham Dinh & Yi-Shuai Niu, 2011. "An efficient DC programming approach for portfolio decision with higher moments," Computational Optimization and Applications, Springer, vol. 50(3), pages 525-554, December.
    6. Onour, Ibrahim, 2008. "Forward-Looking Beta Estimates:Evidence from an Emerging Market," MPRA Paper 14992, University Library of Munich, Germany.
    7. Ángel León & Gonzalo Rubio & Gregorio Serna, 2004. "Autoregressive Conditional Volatility, Skewness And Kurtosis," Working Papers. Serie AD 2004-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Andrei Leonidov & Vladimir Trainin & Alexander Zaitsev & Sergey Zaitsev, 2006. "Market Mill Dependence Pattern in the Stock Market: Asymmetry Structure, Nonlinear Correlations and Predictability," Papers physics/0601098,, revised Jan 2006.
    9. Dr. Ibrahim Onour, "undated". "The Global Financial Crisis and Equity Markets in Middle East Oil Exporting Countries," API-Working Paper Series 1009, Arab Planning Institute - Kuwait, Information Center.

    More about this item


    Garch; stock indices; exchange rates; interest rates; SNOPT; VaR;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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