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Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails

Author

Listed:
  • Xin Zhang

    (VU University Amsterdam)

  • Drew Creal

    (VU University Amsterdam)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

Abstract

We propose a new model for dynamic volatilities and correlations of skewed and heavy-tailed data. Our model endows the Generalized Hyperbolic distribution with time-varying parameters driven by the score of the observation density function. The key novelty in our approach is the fact that the skewed and fat-tailed shape of the distribution directly affects the dynamic behavior of the time-varying parameters. It distinguishes our approach from familiar alternatives such as the generalized autoregressive conditional heteroskedasticity model and the dynamic conditional correlation model where distributional assumptions affect the likelihood but not the parameter dynamics. We present a modified expectation-maximization algorithm to estimate the model. Simulated and empirical evidence shows that the model outperforms its close competitors if skewness and kurtosis are relevant features of the data.

Suggested Citation

  • Xin Zhang & Drew Creal & Siem Jan Koopman & Andre Lucas, 2011. "Modeling Dynamic Volatilities and Correlations under Skewness and Fat Tails," Tinbergen Institute Discussion Papers 11-078/2/DSF22, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20110078
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    References listed on IDEAS

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    7. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    8. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    9. Mencia, Javier F. & Sentana, Enrique, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
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    11. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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    Citations

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    Cited by:

    1. Caballero, Diego & Lucas, André & Schwaab, Bernd & Zhang, Xin, 2020. "Risk endogeneity at the lender/investor-of-last-resort," Journal of Monetary Economics, Elsevier, vol. 116(C), pages 283-297.
    2. Francisco Blasques & Siem Jan Koopman & Andre Lucas, 2012. "Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes," Tinbergen Institute Discussion Papers 12-059/4, Tinbergen Institute.
    3. Bao, Te & Diks, Cees & Li, Hao, 2018. "A generalized CAPM model with asymmetric power distributed errors with an application to portfolio construction," Economic Modelling, Elsevier, vol. 68(C), pages 611-621.
    4. André Lucas & Bernd Schwaab & Xin Zhang, 2017. "Modeling Financial Sector Joint Tail Risk in the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 171-191, January.
    5. Bernd Schwaab, 2012. "Conditional probabilities and contagion measures for euro area sovereign default risk," Research Bulletin, European Central Bank, vol. 17, pages 6-11.
    6. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    7. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    8. Schwaab, Bernd & Lucas, André & Zhang, Xin, 2013. "Conditional and joint credit risk," Working Paper Series 1621, European Central Bank.
    9. Jouchi Nakajima, 2017. "Bayesian analysis of multivariate stochastic volatility with skew return distribution," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 546-562, May.
    10. Andre Lucas & Bernd Schwaab & Xin Zhang, 2013. "Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics," Tinbergen Institute Discussion Papers 13-063/IV/DSF56, Tinbergen Institute, revised 13 Oct 2014.

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    More about this item

    Keywords

    Dynamic conditional correlations; Generalized Hyperbolic distributions; Observation driven models;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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