IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0290.html
   My bibliography  Save this article

Joint distribution of stock indices: Methodological aspects of construction and selection of copula models

Author

Listed:
  • Alexander Knyazev

    (Astrakhan State University, Astrakhan, Russian Federation)

  • Oleg Lepekhin

    (Astrakhan State University, Astrakhan, Russian Federation)

  • Arkady Shemyakin

    (University of St. Thomas, St. Paul, USA)

Abstract

The paper discusses the practical aspects of modeling joint distribution of pairs of national stock indices via copula functions. Parameters of marginal distributions and the association parameter describing the dependence structure are estimated using empirical Bayes method numerically implemented with the help of random walk Metropolis algorithm. A comparison of parametric and semiparametric approaches to copula model construction is performed. The problem of selection of a class of pair copula functions approximating such empirical characteristics of stock indices dependence as Kendall’s concordance, joint empirical cumulative distribution function, and tail behavior.

Suggested Citation

  • Alexander Knyazev & Oleg Lepekhin & Arkady Shemyakin, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 30-53.
    • Handle: RePEc:ris:apltrx:0290
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2016_42_030-053.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g70969520 is not listed on IDEAS
    2. Marius Hofert & Matthias Scherer, 2011. "CDO pricing with nested Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 775-787.
    3. T. Ane & L. Ureche-Rangau, 2008. "Time-varying conditional dependence in chinese stock markets," Post-Print hal-00578249, HAL.
    4. Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
    5. Coeurdacier, Nicolas & Guibaud, Stéphane, 2011. "International portfolio diversification is better than you think," Journal of International Money and Finance, Elsevier, vol. 30(2), pages 289-308, March.
    6. Twm Evans & David G. McMillan, 2009. "Financial co-movement and correlation: evidence from 33 international stock market indices," International Journal of Banking, Accounting and Finance, Inderscience Enterprises Ltd, vol. 1(3), pages 215-241.
    7. Hu, Jian, 2008. "Dependence Structures in Chinese and U.S. Financial Markets -- A Time-varying Conditional Copula Approach," MPRA Paper 11401, University Library of Munich, Germany.
    8. EnDer Su, 2017. "Measuring and Testing Tail Dependence and Contagion Risk Between Major Stock Markets," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 325-351, August.
    9. Dean Fantazzini, 2011. "Analysis of multidimensional probability distributions with copula functions. II," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 23(3), pages 98-132.
    10. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g70969520 is not listed on IDEAS
    11. 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.
    12. Geert Bekaert & Robert J. Hodrick & Xiaoyan Zhang, 2009. "International Stock Return Comovements," Journal of Finance, American Finance Association, vol. 64(6), pages 2591-2626, December.
    13. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    14. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    15. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    16. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    17. Thierry Ane & Loredana Ureche-Rangau & Chiraz Labidi-Makni, 2008. "Time-varying conditional dependence in Chinese stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 18(11), pages 895-916.
    18. Efim Bronshtein & Elena Prokudina & Anna Gerasimova & Ksenya Dubinskaya, 2011. "Estimation of the interdependence of time series of stocks prices based on copula," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 22-31.
    19. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    20. You, Leyuan & Daigler, Robert T., 2010. "Is international diversification really beneficial?," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 163-173, January.
    21. Ines Fortin & Christoph Kuzmics, 2002. "Tail‐dependence in stock‐return pairs," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 89-107, April.
    22. repec:spo:wpmain:info:hdl:2441/c8dmi8nm4pdjkuc9g70969520 is not listed on IDEAS
    23. Anil Sharma & Neha Seth, 2012. "Literature review of stock market integration: a global perspective," Qualitative Research in Financial Markets, Emerald Group Publishing Limited, vol. 4(1), pages 84-122, April.
    24. Puzanova, Natalia, 2011. "A hierarchical Archimedean copula for portfolio credit risk modelling," Discussion Paper Series 2: Banking and Financial Studies 2011,14, Deutsche Bundesbank.
    25. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    26. Dean Fantazzini, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 100-130.
    27. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    28. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    29. Yury Blagoveschensky, 2012. "Basics of copula’s theory," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 26(2), pages 113-130.
    30. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    31. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g70969520 is not listed on IDEAS
    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. Andrey Bedin & Alexander Kulikov & Andrey Polbin, 2023. "Copula-Based Modelling of Relationship Between Dollar/Rouble Exchange Rate and Oil Prices," Russian Journal of Money and Finance, Bank of Russia, vol. 82(3), pages 87-109, September.

    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. Alexandr Travkin, 2013. "Pair copula constructions in portfolio optimization ploblem," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 32(4), pages 110-133.
    2. Alexey Balaev, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 90-110.
    3. 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.
    4. Travkin, A., 2015. "Estimating Pair-Copula Constructions Using Empirical Tail Dependence Functions: an Application to Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 39-55.
    5. Dean Fantazzini, 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.
    6. 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.
    7. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    8. Kellner, Ralf & Rösch, Daniel, 2019. "A country specific point of view on international diversification," Journal of International Money and Finance, Elsevier, vol. 98(C), pages 1-1.
    9. Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1511-1527.
    10. Yao Axel Ehouman, 2020. "Dependence structure between oil price volatility and sovereign credit risk of oil exporters: Evidence using a Copula Approach," EconomiX Working Papers 2020-31, University of Paris Nanterre, EconomiX.
    11. Yao Axel Ehouman, 2021. "Dependence structure between oil price volatility and sovereign credit risk of oil exporters : Evidence using a Copula Approach," Post-Print hal-03348410, HAL.
    12. 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.
    13. Anubha Goel & Aparna Mehra, 2019. "Analyzing Contagion Effect in Markets During Financial Crisis Using Stochastic Autoregressive Canonical Vine Model," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 921-950, March.
    14. Ehouman, Yao Axel, 2021. "Dependence structure between oil price volatility and sovereign credit risk of oil exporters: Evidence using a copula approach," International Economics, Elsevier, vol. 168(C), pages 76-97.
    15. Xun Lu & Kin Lai & Liang Liang, 2014. "Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model," Annals of Operations Research, Springer, vol. 219(1), pages 333-357, August.
    16. Bassetti, Federico & De Giuli, Maria Elena & Nicolino, Enrica & Tarantola, Claudia, 2018. "Multivariate dependence analysis via tree copula models: An application to one-year forward energy contracts," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1107-1121.
    17. Nguyen, Hoang & Virbickaitė, Audronė, 2023. "Modeling stock-oil co-dependence with Dynamic Stochastic MIDAS Copula models," Energy Economics, Elsevier, vol. 124(C).
    18. Chen, Wei-Peng & Choudhry, Taufiq & Wu, Chih-Chiang, 2013. "The extreme value in crude oil and US dollar markets," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 191-210.
    19. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    20. Mensah, Jones Odei & Premaratne, Gamini, 2014. "Dependence patterns among Banking Sectors in Asia: A Copula Approach," MPRA Paper 60119, University Library of Munich, Germany.

    More about this item

    Keywords

    copula; stock indices; empirical Bayes; semiparametric approach; Metropolis algorithm;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    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:ris:apltrx:0290. 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: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

    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.