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Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae

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  • Katja Ignatieva

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  • Eckhard Platen

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Abstract

This paper examines international equity market co-movements using time-varying copulae. We examine distributions from the class of Symmetric Generalized Hyperbolic (SGH) distributions for modelling univariate marginals of equity index returns. We show based on the goodness-of-fit testing that the SGH class outperforms the normal distribution, and that the Student-t assumption on marginals leads to the best performance, and thus, can be used to fit multivariate copula for the joint distribution of equity index returns. We show in our study that the Student-t copula is not only superior to the Gaussian copula, where the dependence structure relates to the multivariate normal distribution, but also out performs some alternative mixture copula models which allow to reflect asymmetric dependencies in the tails of the distribution. The Student-t copula with Student-t marginals allows to model realistically simultaneous co-movements and to capture tail dependency in the equity index returns. From the point of view of risk management, it is a good candidate for modelling the returns arising in an international equity index portfolio where the extreme losses are known to have a tendency to occur simultaneously. We apply copulae to the estimation of the Value-at-Risk and the Expected Shortfall, and show that the Student-t copula with Student-t marginals is superior to the alternative copula models investigated, as well the Riskmetics approach.
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Suggested Citation

  • Katja Ignatieva & Eckhard Platen, 2010. "Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(3), pages 261-302, September.
  • Handle: RePEc:kap:apfinm:v:17:y:2010:i:3:p:261-302
    DOI: 10.1007/s10690-010-9116-2
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    References listed on IDEAS

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    1. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Frahm, Gabriel & Junker, Markus & Szimayer, Alexander, 2003. "Elliptical copulas: applicability and limitations," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 275-286, July.
    4. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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    6. Clive W. J. Granger, 2003. "Time Series Concepts for Conditional Distributions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 689-701, December.
    7. Fang, Hong-Bin & Fang, Kai-Tai & Kotz, Samuel, 2002. "The Meta-elliptical Distributions with Given Marginals," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 1-16, July.
    8. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    9. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    10. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
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    Citations

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    Cited by:

    1. Ales Kresta & Tomas Tichy, 2012. "International Equity Portfolio Risk Modeling: The Case of the NIG Model and Ordinary Copula Functions," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(2), pages 141-161, May.
    2. Luca Riccetti, 2013. "A copula–GARCH model for macro asset allocation of a portfolio with commodities," Empirical Economics, Springer, vol. 44(3), pages 1315-1336, June.
    3. Ignatieva, Katja & Landsman, Zinoviy, 2015. "Estimating the tails of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 172-186.
    4. Bussière, Matthieu & Hoerova, Marie & Klaus, Benjamin, 2015. "Commonality in hedge fund returns: Driving factors and implications," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 266-280.
    5. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    6. repec:ipg:wpaper:2014-094 is not listed on IDEAS
    7. Heni Boubaker & Nadia Sghaier, 2014. "On the dynamic dependence between US and other developed stock markets: An extreme-value time-varying copula approach," Working Papers 2014-281, Department of Research, Ipag Business School.
    8. Heni Boubaker & Nadia Sghaier, 2014. "On the dynamic dependence between US and other developed stock markets: An extreme," Working Papers 2014-94, Department of Research, Ipag Business School.

    More about this item

    Keywords

    International equity market; Student-t distribution; Symmetric generalized hyperbolic distribution; Time-varying copula; Value-at-risk; World stock index;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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