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Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula

Received: 18 April 2015     Accepted: 29 April 2015     Published: 23 May 2015
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Abstract

In this paper, we establish GJR-GARCH models to extract the residuals of logarithmic returns of two index--- New York stock exchange composite index (NYA) and NASDAQ. and estimate the distribution function of the residuals utilizing Gaussian kernel method and Extreme Value Theory. The kernel cumulative distribution function estimates are well suited for the interior of the distribution where most of the residuals are found and the POT method of Extreme Value Theory fits the extreme residuals in upper and lower tails well. The monte carlo technique is used to simulate the income of securities index 20000 times after we get the marginal distribution of the residual income of securities index. Secondly, By using the copula function to get the joint distribution of mthe two stock index. Lastly, According to the theory of VAR calculate VAR value of the portfolio consisting of two equal weight comprehensive index in different confidence levels.

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3)
DOI 10.11648/j.sjams.20150303.16
Page(s) 136-143
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Extreme Value Theory, VAR Model, GJR-GARCH

References
[1] Andrey I. Kibzun, Evgeniy A. Kuznetsov. Analysis of criteria VaR and CVaR,. Nournal of Banking & Finance, 2006 (30): 779-796.
[2] Le Lei, Sulin Pang, An Empirical Research on the Chinese stock market based on 'VaR, 2007 IEEE International Conference on Control and Automation, 2007:2729-2734.
[3] Yau Man Zeto SamueLValue at risk and conditional extreme value theory via mark:ov regime switching models, The Journal of Futures Markets, 2008(28):155-181.
[4] Alexandra Costello, Ebenezer Asem, Eldon Gardner. Comparison of Historically Simulated VaR: Evidence from Oil Prices, Energy Economics, 2008(10):1600-1623.
[5] Allan Gregory, Jonathan Reeves. Interpreting value at risk (VaR) forecasts, 2007(3):1-20.
[6] Malay Bhattacharyya, Gopal Ritolia. Conditional VaR using EVT Towards a planned margin scheme, International Review of Financial Analysis, 2008(17):382-395.
[7] Michael Mcaleer, Bernardo Do Veiga. Forecasting Value-at-Risk with a Parsimonious Portfolio Spillover GARCH(PS-GARCH) Model, Journal of Forecasting, 2008(27):1-19.
[8] Jenkinson A F. The frequency distribution of the annual maximum(or mimimum) values of meteorological elements, Quarterly Journal of the Royal meteorological society,1955(81):145-158.
[9] Christian Genest, Jock MacKay. The Joy of Copulas: Bivariate Distributions with Uniform Marginals, The American Statistician, 1986(40): 280-283.
[10] Joe H, Multivariate Models and Dependence Concepts. 2004: Chapaman & Hall.
[11] Umberto Cherubim, Elisa Luciano, Walter Vecchiato, Copula Methods in Finance;. 2004: John Wiley & Sons.
[12] Ming Heng Zhang, Qian Sheng Cheng, An approach to VaR for capital markets with Gaussian mixture, Applied Mathematics and Computation, 2005(168):1079-1085.
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Cite This Article
  • APA Style

    Hong Zhang, Li Zhou, Shucong Ming, Yanming Yang, Mengdan Zhou. (2015). Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula. Science Journal of Applied Mathematics and Statistics, 3(3), 136-143. https://doi.org/10.11648/j.sjams.20150303.16

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    ACS Style

    Hong Zhang; Li Zhou; Shucong Ming; Yanming Yang; Mengdan Zhou. Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula. Sci. J. Appl. Math. Stat. 2015, 3(3), 136-143. doi: 10.11648/j.sjams.20150303.16

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    AMA Style

    Hong Zhang, Li Zhou, Shucong Ming, Yanming Yang, Mengdan Zhou. Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula. Sci J Appl Math Stat. 2015;3(3):136-143. doi: 10.11648/j.sjams.20150303.16

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  • @article{10.11648/j.sjams.20150303.16,
      author = {Hong Zhang and Li Zhou and Shucong Ming and Yanming Yang and Mengdan Zhou},
      title = {Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {3},
      number = {3},
      pages = {136-143},
      doi = {10.11648/j.sjams.20150303.16},
      url = {https://doi.org/10.11648/j.sjams.20150303.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.16},
      abstract = {In this paper, we establish GJR-GARCH models to extract the residuals of logarithmic returns of two index--- New York stock exchange composite index (NYA) and NASDAQ. and estimate the distribution function of the residuals utilizing Gaussian kernel method and Extreme Value Theory. The kernel cumulative distribution function estimates are well suited for the interior of the distribution where most of the residuals are found and the POT method of Extreme Value Theory fits the extreme residuals in upper and lower tails well. The monte carlo technique is used to simulate the income of securities index 20000 times after we get the marginal distribution of the residual income of securities index. Secondly, By using the copula function to get the joint distribution of mthe two stock index. Lastly, According to the theory of VAR calculate VAR value of the portfolio consisting of two equal weight comprehensive index in different confidence levels.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula
    AU  - Hong Zhang
    AU  - Li Zhou
    AU  - Shucong Ming
    AU  - Yanming Yang
    AU  - Mengdan Zhou
    Y1  - 2015/05/23
    PY  - 2015
    N1  - https://doi.org/10.11648/j.sjams.20150303.16
    DO  - 10.11648/j.sjams.20150303.16
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 136
    EP  - 143
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20150303.16
    AB  - In this paper, we establish GJR-GARCH models to extract the residuals of logarithmic returns of two index--- New York stock exchange composite index (NYA) and NASDAQ. and estimate the distribution function of the residuals utilizing Gaussian kernel method and Extreme Value Theory. The kernel cumulative distribution function estimates are well suited for the interior of the distribution where most of the residuals are found and the POT method of Extreme Value Theory fits the extreme residuals in upper and lower tails well. The monte carlo technique is used to simulate the income of securities index 20000 times after we get the marginal distribution of the residual income of securities index. Secondly, By using the copula function to get the joint distribution of mthe two stock index. Lastly, According to the theory of VAR calculate VAR value of the portfolio consisting of two equal weight comprehensive index in different confidence levels.
    VL  - 3
    IS  - 3
    ER  - 

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Author Information
  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • Chinese Academy of Finance and Development, Central University of Finance and Economics, Beijing, China

  • Information Technology Department, East China Institute of Technology, Nanchang, China

  • School of Media Studies and Humanities, Zhejiang University City College, Hangzhou, China

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