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An Econometric Study of Vine Copulas

Author

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  • Dominique Guegan

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

  • Pierre-André Maugis

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present a new recursive algorithm to construct vine copulas based on an underlying tree structure. This new structure is interesting to compute multivariate distributions for dependent random variables. We proove the asymptotic normality of the vine copula parameter estimator and show that all vine copula parameter estimators have comparable variance. Both results are crucial to motivate any econometrical work based on vine copulas. We provide an application of vine copulas to estimate the VaR of a portfolio, and show they offer significant improvement as compared to a benchmark estimator based on a GARCH model.

Suggested Citation

  • Dominique Guegan & Pierre-André Maugis, 2010. "An Econometric Study of Vine Copulas," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00492124, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00492124 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00492124
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    References listed on IDEAS

    as
    1. Dominique Guegan & Pierre-André Maugis, 2008. "New prospects on vines," Documents de travail du Centre d'Economie de la Sorbonne b08095, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Mar 2010.
    2. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    3. Lorán Chollete & Andréas Heinen & Alfonso Valdesogo, 2009. "Modeling International Financial Returns with a Multivariate Regime-switching Copula," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(4), pages 437-480, Fall.
    4. Andrew J. Patton, 2008. "Copula-Based Models for Financial Time Series," OFRC Working Papers Series 2008fe21, Oxford Financial Research Centre.
    5. Andrew Patton & Yanqin Fan & Xiaohong Chen, 2004. "Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," Working Papers wp04-19, Warwick Business School, Finance Group.
    6. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    7. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    8. Fischer, Matthias J. & Köck, Christian & Schlüter, Stephan & Weigert, Florian, 2007. "Multivariate Copula Models at Work: Outperforming the desert island copula?," Discussion Papers 79/2007, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
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    Citations

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    Cited by:

    1. Dominique Guegan & Bertrand Hassani, 2016. "Combining risk measures to overcome their limitations - spectrum representation of the sub-additivity issue, distortion requirement and added-value of the Spatial VaR solution: An application to Regul," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01391103, HAL.
    2. Dominique Guegan & Bertrand Hassani, 2011. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Documents de travail du Centre d'Economie de la Sorbonne 11017r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2011.
    3. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01467857, HAL.
    4. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00951593, HAL.
    5. repec:hal:journl:halshs-00587706 is not listed on IDEAS
    6. Dominique Guegan & Bertrand K. Hassani, 2016. "Combining risk measures to overcome their limitations - spectrum representation of the sub-additivity issue, distortion requirement and added-value of the Spatial VaR solution: An application to Regul," Documents de travail du Centre d'Economie de la Sorbonne 16066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Dominique Guegan & Bertrand Hassani, 2011. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Documents de travail du Centre d'Economie de la Sorbonne 11017rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
    8. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
    9. Dominique Guegan & Bertrand K. Hassani, 2016. "Risk Measures At Risk- Are we missing the point? Discussions around sub-additivity and distortion," Documents de travail du Centre d'Economie de la Sorbonne 16039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Dominique Guegan & Bertrand K. Hassani, 2016. "Risk Measures At Risk- Are we missing the point? Discussions around sub-additivity and distortion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318093, HAL.
    11. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    Keywords

    copules multivariées; gestion des risques.; Vines; multivariate copulas; risk management.;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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