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Hierarchies of Archimedean copulas

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  • Cornelia Savu
  • Mark Trede

Abstract

We present a flexible class of hierarchical copulas capable of modelling multidimensional joint distributions of asset returns with a richer rank correlation structure than existing models. We derive estimators and simulation techniques. The methods are applied to an illustrative portfolio consisting of a subset of DAX stocks.

Suggested Citation

  • Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
  • Handle: RePEc:taf:quantf:v:10:y:2010:i:3:p:295-304 DOI: 10.1080/14697680902821733
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 22(2), pages 98-134.
    2. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Calabrese, Raffaella & Degl’Innocenti, Marta & Osmetti, Silvia Angela, 2017. "The effectiveness of TARP-CPP on the US banking industry: A new copula-based approach," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1029-1037.
    4. Brechmann Eike Christain & Czado Claudia, 2013. "Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 307-342, December.
    5. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, pages 131-152.
    6. Härdle Wolfgang Karl & Okhrin Ostap & Okhrin Yarema, 2013. "Dynamic structured copula models," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 361-388, December.
    7. Göran Kauermann & Renate Meyer, 2014. "Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas," Computational Statistics, Springer, vol. 29(1), pages 283-306, February.
    8. Zhu, Wenjun & Wang, Chou-Wen & Tan, Ken Seng, 2016. "Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 20-36.
    9. Manner, Hans & Türk, Dennis & Eichler, Michael, 2016. "Modeling and forecasting multivariate electricity price spikes," Energy Economics, Elsevier, vol. 60(C), pages 255-265.
    10. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    11. Enrico Bernardi & Silvia Romagnoli, 2016. "Distorted Copula-Based Probability Distribution of a Counting Hierarchical Variable: A Credit Risk Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., pages 285-310.
    12. Andreas Masuhr, 2017. "Volatility Transmission in Overlapping Trading Zones," CQE Working Papers 6717, Center for Quantitative Economics (CQE), University of Muenster.
    13. Ostap Okhrin & Alexander Ristig, 2012. "Hierarchical Archimedean Copulae: The HAC Package," SFB 649 Discussion Papers SFB649DP2012-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    15. Lee, Sangwook & Kim, Min Jae & Kim, Soo Yong, 2011. "Interest rates factor model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2531-2548.
    16. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, pages 52-69.
    17. Bernardi, Enrico & Falangi, Federico & Romagnoli, Silvia, 2015. "A hierarchical copula-based world-wide valuation of sovereign risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 155-169.
    18. Bernardi Enrico & Romagnoli Silvia, 2015. "A copula-based hierarchical hybrid loss distribution," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 73-87, April.
    19. Grothe, Oliver & Hofert, Marius, 2015. "Construction and sampling of Archimedean and nested Archimedean Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 182-198.
    20. repec:eee:ecofin:v:42:y:2017:i:c:p:193-217 is not listed on IDEAS

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