The Application And Comparison Of VaR Models In Chinese Stock Market Based On Extreme Value Theory

Nowadays, most of the empirical studies and models concern average properties like expected returns, volatility, or correlations, and little attention has been given to the extreme movements. However, a lot of lessons have told us that neglecting extreme risk will cause huge loss, and we must find certain tool to reflect and estimate it correctly. Extreme value theory (EVT) is one of the best choices, which can effectively forecast and guard against the financial risk. This article presents an application of extreme value theory to compute the value at risk of Chinese stock market.Firstly, this article talks about some basic idea on the VaR, such as its definition, application and some traditional ways to compute it. Secondly the representative studies from foreign and domestic scholars are systematically summarized. Then this article introduces the principle of EVT, and based on these theories, three VaR models are discussed, including the different ways on estimating the parameters. Thirdly, these EVT-VaR models are applied to the study on Chinese stock index daily returns. Through the application and comparison, some results were found: (1) The traditional ways to compute the VaR will underestimate the potential risk, so they are not effective, especially when used to analyzing the extreme risk; (2) BMM model can accurately reflect the tail of the distribution of stock index minimum and maximum daily returns; (3) GPD model is not as good as expectation, but its combination with GARCH model can raise the accuracy of forecasting; (4) The empirical study discovered that the tail of the distribution of stock index maximum daily returns follows Frechet distribution, and the tail of the distribution of stock index minimum daily returns follows Gumbel distribution. (5) The tail of the distribution of stock index daily returns will change with time. Based on EVT, the accurate estimator of VaR was got, which is very helpful in analyzing the extreme movements. At the last, this part discusses the further development of the research on EVT, and summarizes the whole article.