Based On Value At Risk Of Extreme Value Theory And Its Empirical Analysis

Accurate measure of risk is the key issue of financial risk management, today among a variety of ways to measure risk in the financial markets, VaR(Value at Risk) that show the various factors of risk by VaR values-a specific figure-is applied more extensively, So you can compare the size of the risk.Relative to the traditional method, Value at risk requires assumption on the distribution type of financial series, while VaR calculations based POT model of Extreme Value Theory require no assumption which reduces the error caused by estimating the model distribution, then further optimization of the results.The paper uses POT model based on extreme theory to estimate VaR, for that when doing this, it is often assumed into independent identically distributed for the data over threshold value, and however, financial sequence is not independent but often with an autocorrelation and fluctuation in fact-a great value occurs in the series, then gathering a sequence of great value nearby and existing an autocorrelation between data. To sufficiently large threshold, adjacent excess non-independent. In this way, the actual situation will not consistent with the initial hypothesis, and there will be larger deviation between the resulting VaR values and actual ones, and result in certain risks in the actual application. Therefore against this shortcoming, this article proposes the method of combining ARMA-EGARCH model and extreme value theory to calculate VaR on the basis of traditional description of the individual use of tail characteristics of financial returns. First, it models financial data using ARMA model. Second, it obtains approximate independent and identically distributed residuals sequence using EGARCH model to capture the autocorrelation in the residuals and heteroskedasticity phenomenon. Then, analyze the residual sequence after filtration using traditional Extreme Value Theory and then calculate VaR according to exiting results. Doing like this can maximize eliminate errors caused by partial correlation of data, and thus estimate a relatively accurate of the VaR.There is an empirical analysis on the Shanghai Index and Shenzhen indices of the stock market from August 13,1999 to August 14,2009 to verify that the VaR value calculated by improved model is more reasonable, and the estimate accuracy gain improvement, compare the size of the risks between both of the stock market and have more important reference value and significance in the forecasts of financial risk for financial institutions and individual investors.