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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
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    File URL: http://www.e-finanse.com/artykuly_eng/180.pdf
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    References listed on IDEAS

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    1. 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.
    2. John Davis, 2005. "Introduction," Journal of Economic Methodology, Taylor & Francis Journals, vol. 12(3), pages 361-361.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    7. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    copula function; GARCH model; conditional copula; DCC-MVGARCH; dynamic conditional copula; bootstrap;

    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

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