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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
Authors
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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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.
Keywords
Extreme Value Theory, VAR Model, GJR-GARCH
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
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