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Modeling Dependencies in Finance using Copulae

Author

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  • Wolfgang Härdle
  • Ostap Okhrin
  • Yarema Okhrin

Abstract

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.

Suggested Citation

  • Wolfgang Härdle & Ostap Okhrin & Yarema Okhrin, 2008. "Modeling Dependencies in Finance using Copulae," SFB 649 Discussion Papers SFB649DP2008-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2008-043
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-043.pdf
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    References listed on IDEAS

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    1. Pierre Cahuc & André Zylberberg, 2004. "Labor Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 026203316x, January.
    2. repec:eee:labchp:v:2:y:1986:i:c:p:1139-1181 is not listed on IDEAS
    3. Froot, Kenneth A., 1989. "Consistent Covariance Matrix Estimation with Cross-Sectional Dependence and Heteroskedasticity in Financial Data," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(03), pages 333-355, September.
    4. Rick L. Williams, 2000. "A Note on Robust Variance Estimation for Cluster-Correlated Data," Biometrics, The International Biometric Society, vol. 56(2), pages 645-646, June.
    5. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
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    Cited by:

    1. Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing, vol. 70(2), pages 267-284, August.
    2. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Raushan Bokusheva, 2011. "Measuring dependence in joint distributions of yield and weather variables," Agricultural Finance Review, Emerald Group Publishing, vol. 71(1), pages 120-141, May.

    More about this item

    Keywords

    Distribution functions; Dimension Reduction; Risk management; Statistical models;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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