Research On China Stock Index And Its' Value At Risk By G-ARMA-GARCH Family Based On Stable Distribution

Data in the financial markets generally have fat-tailed features.Data generally has the character of volatility in the stock market.The different development level of the stock market generally exists asymmetry,heteroscedasticity,aggregation effect and lever-age effect.Therefore,how to study the fat-tailed and other features of stock data is a key problem.The fat-tailed characteristics and asymmetry of stock index returns in Shanghai and Shenzhen stock markets are captured by the stable distribution.The het-eroscedasticity is captured by the ARMA-GARCH model.The research structure is as follows:This paper firstly introduce the general characteristics of financial market data,and the commonly used fitting distribution and characteristics of these distributions.Then it gives the definition of stable distribution from stabilization,central-limit theorem and feature function,describes the nature of the stable distribution detailly and Baysian estimation method.With the help of stable distribution density function figures,we can strengthen the intuitive understanding of st,able distribution.The fourth chapter of this paper introduces the gradient factor.Combined with stable distribution,we build G-ARMA-GARCH-S model family based on stable distri-bution,and discussed the characteristics of G-ARMA-GARCH model family based on several distributions.Then we use the maximum likelihood estimation to estimate the model coefficients and give the value at risk(VaR)estimation method based on stable distribution.VaR is a tool to measure the market risk.Finally,we verified that Baysian estimation is more precise than other estimation methods on stable distribution parameter estimation.we do empirical analysis through the Shanghai and Shenzhen stock market index.We found that G-ARMA-GARCH-S model family is better than other models based on normal distribution with thin tailed character,and the estimated VaR within G-ARMA-GARCH-S model family depicts fi-nancial market risk more accurately.It can be useful for investors.