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Modeling dependencies in finance using copulae

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  • Härdle, Wolfgang Karl
  • Okhrin, Ostap
  • Okhrin, Yarema

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 copulae 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

  • Härdle, Wolfgang Karl & Okhrin, Ostap & Okhrin, Yarema, 2008. "Modeling dependencies in finance using copulae," SFB 649 Discussion Papers 2008-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2008-043
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    References listed on IDEAS

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    Cited by:

    1. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    2. Raushan Bokusheva, 2011. "Measuring dependence in joint distributions of yield and weather variables," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 71(1), pages 120-141, May.
    3. Liu, X. & Xu, W. & Odening, M., 2011. "Lassen sich Ertragsrisiken in der Landwirtschaft global diversifizieren?," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 46, March.
    4. Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 70(2), pages 267-284, August.
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    More about this item

    Keywords

    Distribution functions; dimension reduction; risk management; statistical models;
    All these keywords.

    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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