Asia-Pacific Financial Markets

, Volume 17, Issue 3, pp 261–302 | Cite as

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

  • Katja Ignatieva
  • Eckhard PlatenEmail author


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 outperforms 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.


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


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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Graduate Program “Finance and Monetary Economics,”Goethe University, House of FinanceFrankfurt am MainGermany
  2. 2.School of Finance and Economics and Department of Mathematical SciencesUniversity of Technology SydneySydneyAustralia

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