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

Hong Zhang; Li Zhou; Shucong Ming; Yanming Yang; Mengdan Zhou

doi:doi:10.11648/j.sjams.20150303.16

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

Hong Zhang, Li Zhou, Shucong Ming, Yanming Yang, Mengdan Zhou

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.

DOI	10.11648/j.sjams.20150303.16
Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3, June 2015)
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), 2024. Published by Science Publishing Group

Keywords

Extreme Value Theory, VAR Model, GJR-GARCH

References

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[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.
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[13]	Dennis Bams, Thorsten Ixhnert, Christian C.P. Wolff. An evaluation framework for alternative VaR-models, Journal of International Money and Finance, 2005(24):944-958.
[14]	Matthew Pritsker, The Hidden Dangers of Historical Simulation, Journal of Banking & Finance, 2006(30):561-582.

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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

Hong Zhang

School of Information, Beijing Wuzi University, Beijing, China
Li Zhou

School of Information, Beijing Wuzi University, Beijing, China
Shucong Ming

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

Information Technology Department, East China Institute of Technology, Nanchang, China
Mengdan Zhou

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download