IDEAS home Printed from https://ideas.repec.org/a/rze/efinan/v7y2011i2p1-16.html
   My bibliography  Save this article

Modeling Stock Market Indexes With Copula Functions

Author

Listed:
  • Jacek Leskow

    (Wyzsza Szkola Biznesu National-Louis University in Nowy Sacz)

  • Justyna Mokrzycka

    (Wyzsza Szkola Biznesu National-Louis University in Nowy Sacz)

  • Krzysztof Krawiec

    (Wyzsza Szkola Biznesu National-Louis University in Nowy Sacz)

Abstract

Contemporary financial risk management is significantly based on the analysis of time series of returns. One of the most significant errors frequently committed by analysts is the predominant use of normal distributions when it is clear that the returns are not normal. Copula models and models for non-normal multivariate distributions provide new tools to solve the problem because the obtained results are immediately applicable in portfolio management, option pricing and measuring risk without assuming normality. Therefore, both a theoretician and a practitioner are interested in multivariate models for returns and copula functions. The copula function models provide an effective and interesting technique of constructing multivariate distribution starting from marginal ones. Due to Sklar's result established in 1959, we can present any multivariate distribution with a help of corresponding marginal distributions and a selected copula function. In this work we present an application of copula function to construct multivariate conditional distributions of times series. In the last part of this paper dynamic models such as DCC-MVGARCH and conditional copula are analyzed. Moreover, we also present an application of bootstrap in the context of copula function. This work is appended by examples showing practical application of our work.

Suggested Citation

  • Jacek Leskow & Justyna Mokrzycka & Krzysztof Krawiec, 2011. "Modeling Stock Market Indexes With Copula Functions," "e-Finanse", University of Information Technology and Management, Institute of Financial Research and Analysis, vol. 7(2), pages 1-16, August.
    • Handle: RePEc:rze:efinan:v:7:y:2011:i:2:p:1-16
    as

    Download full text from publisher

    File URL: http://www.e-finanse.com/artykuly_eng/180.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    2. 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.
    3. Rob van den Goorbergh, 2004. "A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets," DNB Working Papers 022, Netherlands Central Bank, Research Department.
    4. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. 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..
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    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. Alistair Mees & Berndt Pilgram, 2000. "Non-Linear Markov Modelling Using Canonical Variate Analysis: Forecasting Exchange Rate Volatility," Econometric Society World Congress 2000 Contributed Papers 1162, Econometric Society.
    2. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    3. Loredana Ureche-Rangau & Quiterie de Rorthays, 2009. "More on the volatility-trading volume relationship in emerging markets: The Chinese stock market," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 779-799.
    4. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.).
    5. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    6. Bodnar, Taras & Hautsch, Nikolaus, 2012. "Copula-based dynamic conditional correlation multiplicative error processes," SFB 649 Discussion Papers 2012-044, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    8. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    9. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    10. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
    11. S. M. Abdullah & Salina Siddiqua & Muhammad Shahadat Hossain Siddiquee & Nazmul Hossain, 2017. "Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 3(1), pages 1-19, December.
    12. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    13. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    14. Michael McKenzie & Heather Mitchell & Robert Brooks & Robert Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 22-38.
    15. Debabrata Mukhopadhyay & Nityananda Sarkar, 2013. "Stock Returns Under Alternative Volatility and Distributional Assumptions: The Case for India," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 1-19, April.
    16. Djahoué Mangblé Gérald, 2018. "Estimating and Forecasting West Africa Stock Market Volatility Using Asymmetric GARCH Models," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 8(6), pages 1-4.
    17. Kumar Arya & Sahoo Jyotirmayee & Sahoo Jyotsnarani & Nanda Subhashree & Debyani Devi, 2024. "Exploring Asymmetric GARCH Models for Predicting Indian Base Metal Price Volatility," Folia Oeconomica Stetinensia, Sciendo, vol. 24(1), pages 105-123.
    18. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    19. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    20. Ricardo Alverola, 2007. "Estimating Volatility Returns Using ARCH Models. An Empirical Case: The Spanish Energy Market," Lecturas de Economía, Universidad de Antioquia, Departamento de Economía, issue 66, pages 251-276, Enero-Jun.

    More about this item

    Keywords

    copula function; GARCH model; conditional copula; DCC-MVGARCH; dynamic conditional copula; bootstrap;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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:rze:efinan:v:7:y:2011:i:2:p:1-16. 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: Pawel Bochenek (email available below). General contact details of provider: https://edirc.repec.org/data/igwsipl.html .

    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.