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.
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