Dynamic VaR Model Based On Extreme Value Theory And Its Application

The financial crisis started in 2008 has caused serious damage to the order of the world's financial markets, leading to collapse of large financial institutions, swings of financial asset price and even the bankruptcy of governments. It takes such experience only one extreme market movements few years or even decades to produce devastating effects that such a large scale, though the financial risk is everywhere and at all times there. Therefore, the development of new and effective risk measurement tool for financial institutions and regulatory authorities in extreme cases is of great significance. Risk, in particular the prevention of such extreme risk as the economy gradually recovered should not be relaxed.This thesis is intended to improve the accuracy and applicability of VaR based on extreme value theory (EVT). As a statistical method of describing extreme changes, extreme value theory only models the tail, rather than the entire distribution. And without assuming a specific distribution type, EVT avoids the model risk. This is one of the major advantages of extreme value theory, but the VaR values based on the extreme value theory model are relatively conservative, this may make some financial institutions have no incentive to use this model to measure risk. In this thesis, three improved dynamic risk measurement models have been proposed.In this thesis, the dynamic VaR measurement models based on EVT is applied to measure China's Shanghai and Shenzhen stock market to analyze the proposed models for the specific situation through the compare of the VaR measured with the traditional method. This thesis is divided into theoretical part and empirical part. Aspects of theoretical research, the related VaR theory, including the definition of VaR, VaR of the traditional method, VaR model accuracy test methods - backtesting and the advantages and disadvantages of VaR has been first introduced. Then based on the extreme value theory models– BMM model and POT model, three dynamic models - GARCH-POT models, GJR-POT model and the EGARCH-POT model have been proposed.In the empirical research part, we choose Shanghai Composite Index and Shenzhen Component Index on a longer return period data as a sample. Its basic statistical analysis shows that, like most financial time series, we selected sample data is fat-tailed and the fluctuations is clustered, which shows the heteroscedasticity. We do not assume a specific distribution of the sample. After fitting the BMM model and the POT model to the sample data, 1-day VaR value is obtained. Then we estimate the parameters of proposed three dynamic VaR measurement models, predict 1-day ahead conditional mean and conditional variance and calculate the median score of standardized residuals with the POT model. The 1-day VaR values based on dynamic VaR measurement models are finally obtained. Then we made a simple and intuitive comparison. But to tell a good model needs to compare dynamically. Finally, the thesis uses the backtesting to test the models, and make a comparison.The results show that, faced with different market situations, different financial institutions or investors need specific VaR measurement tools. The BMM model and the POT model, especially the POT model, are suitable for conservative investors or financial institutions to measure the VaR value at higher confidence levels. While the proposed models have improved the performance of POT model, making it also apply to aggressive financial institutions or investors.