Please enter verification code
Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula
Science Journal of Applied Mathematics and Statistics
Volume 3, Issue 3, June 2015, Pages: 136-143
Received: Apr. 18, 2015; Accepted: Apr. 29, 2015; Published: May 23, 2015
Views 4636      Downloads 183
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
Article Tools
Follow on us
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.
Extreme Value Theory, VAR Model, GJR-GARCH
To cite this article
Hong Zhang, Li Zhou, Shucong Ming, Yanming Yang, Mengdan Zhou, Empirical Research on VAR Model Based on GJR-GARCH, EVT and Copula, Science Journal of Applied Mathematics and Statistics. Vol. 3, No. 3, 2015, pp. 136-143. doi: 10.11648/j.sjams.20150303.16
Andrey I. Kibzun, Evgeniy A. Kuznetsov. Analysis of criteria VaR and CVaR,. Nournal of Banking & Finance, 2006 (30): 779-796.
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.
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.
Alexandra Costello, Ebenezer Asem, Eldon Gardner. Comparison of Historically Simulated VaR: Evidence from Oil Prices, Energy Economics, 2008(10):1600-1623.
Allan Gregory, Jonathan Reeves. Interpreting value at risk (VaR) forecasts, 2007(3):1-20.
Malay Bhattacharyya, Gopal Ritolia. Conditional VaR using EVT Towards a planned margin scheme, International Review of Financial Analysis, 2008(17):382-395.
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.
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.
Christian Genest, Jock MacKay. The Joy of Copulas: Bivariate Distributions with Uniform Marginals, The American Statistician, 1986(40): 280-283.
Joe H, Multivariate Models and Dependence Concepts. 2004: Chapaman & Hall.
Umberto Cherubim, Elisa Luciano, Walter Vecchiato, Copula Methods in Finance;. 2004: John Wiley & Sons.
Ming Heng Zhang, Qian Sheng Cheng, An approach to VaR for capital markets with Gaussian mixture, Applied Mathematics and Computation, 2005(168):1079-1085.
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.
Matthew Pritsker, The Hidden Dangers of Historical Simulation, Journal of Banking & Finance, 2006(30):561-582.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186