IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00492124.html
   My bibliography  Save this paper

An Econometric Study of Vine Copulas

Author

Listed:
  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Pierre-André Maugis

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 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://shs.hal.science/halshs-00492124
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00492124/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    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, Oxford University Press, vol. 7(4), pages 437-480, Fall.
    4. Andrew J. Patton, 2008. "Copula-Based Models for Financial Time Series," Economics Series Working Papers 2008fe21, University of Oxford, Department of Economics.
    5. Chen, Xiaohong & Fan, Yanqin & Patton, Andrew J., 2004. "Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates," LSE Research Online Documents on Economics 24681, London School of Economics and Political Science, LSE Library.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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," 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, 2018. "A novel multivariate risk measure: the Kendall VaR," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01467857, HAL.
    4. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    5. Dominique Guegan & Bertrand K. Hassani, 2016. "Risk Measures At Risk- Are we missing the point? Discussions around sub-additivity and distortion," Post-Print halshs-01318093, HAL.
    6. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Post-Print halshs-01467857, HAL.
    7. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00951593, HAL.
    8. 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," Post-Print halshs-01391103, HAL.
    9. Chebbi, Ali & Hedhli, Amel, 2022. "Revisiting the accuracy of standard VaR methods for risk assessment: Using the Copula–EVT multidimensional approach for stock markets in the MENA region," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 430-445.
    10. Dominique Guegan & Bertrand Hassani, 2012. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Post-Print halshs-00587706, HAL.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Post-Print halshs-00951593, HAL.
    16. 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.
    17. Antonov I. N. & Knyazev A. G. & Lepekhin O. A., 2016. "Copula Models of the Joint Distribution of Exchange Rates," World of economics and management / Vestnik NSU. Series: Social and Economics Sciences, Socionet, vol. 16(4), pages 20-38.
    18. Bukre Yildirim Kulekci & Gulden Poyraz & Ismail Gur & Ozan Evkaya, 2023. "Dependence Analysis of the ISE100 Banking Sector Using Vine Copula," Istanbul Journal of Economics-Istanbul Iktisat Dergisi, Istanbul University, Faculty of Economics, vol. 73(73-1), pages 55-81, June.
    19. 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.
    20. 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 17008r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2018.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dominique Guegan & Pierre-André Maugis, 2011. "An econometric Study for Vine Copulas," PSE-Ecole d'économie de Paris (Postprint) halshs-00645799, HAL.
    2. Dominique Guegan & Pierre-André Maugis, 2011. "An econometric Study for Vine Copulas," Post-Print halshs-00645799, HAL.
    3. Dominique Guegan & Pierre-André Maugis, 2010. "An Econometric Study of Vine Copulas," Post-Print halshs-00492124, HAL.
    4. Pierre-André Maugis & Dominique Guegan, 2010. "Note on new prospects on vines," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00471362, HAL.
    5. Manner, Hans & Alavi Fard, Farzad & Pourkhanali, Armin & Tafakori, Laleh, 2019. "Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae," Energy Economics, Elsevier, vol. 78(C), pages 143-164.
    6. Reboredo, Juan C. & Ugolini, Andrea, 2015. "A vine-copula conditional value-at-risk approach to systemic sovereign debt risk for the financial sector," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 98-123.
    7. Maziar Sahamkhadam & Andreas Stephan, 2019. "Portfolio optimization based on forecasting models using vine copulas: An empirical assessment for the financial crisis," Papers 1912.10328, arXiv.org.
    8. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    9. David E. Allen & Mohammad A. Ashraf & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2013. "Financial dependence analysis: applications of vine copulas," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 403-435, November.
    10. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    11. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    12. Liu, Mengqiao & Zhang, Yu Yvette & Jia, Ruixin, 2024. "Is the Chinese gold product a hedge or safe haven for Chinese overseas investors?," 2024 Annual Meeting, July 28-30, New Orleans, LA 343698, Agricultural and Applied Economics Association.
    13. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    14. Manner, Hans & Stark, Florian & Wied, Dominik, 2019. "Testing for structural breaks in factor copula models," Journal of Econometrics, Elsevier, vol. 208(2), pages 324-345.
    15. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    16. Christoffersen, Peter & Langlois, Hugues, 2013. "The Joint Dynamics of Equity Market Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(5), pages 1371-1404, October.
    17. Chollete, Loran & de la Pena , Victor & Lu, Ching-Chih, 2009. "International Diversification: An Extreme Value Approach," UiS Working Papers in Economics and Finance 2009/26, University of Stavanger.
    18. Chollete, Loran & Ning, Cathy, 2009. "The Dependence Structure of Macroeconomic Variables in the US," UiS Working Papers in Economics and Finance 2009/31, University of Stavanger.
    19. Krupskii, Pavel & Joe, Harry, 2015. "Structured factor copula models: Theory, inference and computation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 53-73.
    20. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.

    More about this item

    Keywords

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

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00492124. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.