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A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets

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Rob van den Goorbergh

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Abstract

This paper investigates the level and development of cross-country stock market dependence using daily returns on stock indices. The use of copulas allows us to build exible models of the joint distribution of stock index returns. In particular, we apply univariate AR(p)-GARCH(1,1) models to the margins with possibly skewed and fat tailed return innovations, while modelling the dependence between markets using parametric families of copulas which offer various alternatives to the commonly assumed normal dependence structure. Moreover, the dependence across stock markets is allowed to vary over time through a GARCH-like autoregressive conditional copula model. Using synchronous daily returns on U.S., U.K., and French stock indices, we find strong evidence that the conditional dependence between pairs of each of these markets varies over time. All market pairs show high levels of dependence persistence. The performance of the copula-based approach is compared with Engle's (2002) dynamic conditional correlation model and found to be superior.

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Paper provided by Netherlands Central Bank, Research Department in its series DNB Working Papers with number 022.

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Date of creation: Dec 2004
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Handle: RePEc:dnb:dnbwpp:022

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Related research
Keywords: stock markets; dependence; copulas; synchronicity;

Find related papers by JEL classification:
G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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    Other versions:
  3. BAUWENS, Luc & LAURENT, SŽbastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  4. Robert F. Engle & Victor Ng & Michael Rothschild, 1988. "Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills," NBER Technical Working Papers 0065, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  5. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August. [Downloadable!] (restricted)
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  6. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December. [Downloadable!]
  7. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June. [Downloadable!] (restricted)
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    Other versions:
  13. 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. [Downloadable!] (restricted)
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    Other versions:
  18. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
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  21. U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor and Francis Journals, vol. 9(2), pages 69-85, June. [Downloadable!] (restricted)
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  23. Robert Engle & Tim Bollerslev, 1986. "Modelling the persistence of conditional variances," Econometric Reviews, Taylor and Francis Journals, vol. 5(1), pages 1-50. [Downloadable!] (restricted)
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  25. Joshua V. Rosenberg, 2003. "Nonparametric pricing of multivariate contingent claims," Staff Reports 162, Federal Reserve Bank of New York. [Downloadable!]
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