Research On Value At Risk Based On Gram-Charlier Dynamic Higher-order Moment

Once the mean variance analysis method was put forward,it became popular in the academic circles and became an important tool for research and practice in the field of financial economy.However,with the development of econometrics,people find that it is not enough to measure risk only by means of mean and variance.This method often underestimates risk.Many studies have shown that the stock return distribution does not obey the normal distribution,but has the characteristics of peak,thick tail and asymmetry.A new distribution is needed to better fit these characteristics,which is closely related to the high-order moment of return.Therefore,scholars gradually turn their attention to the high-order moment modeling.Further,scholars found that the peak and thick tail characteristics of stock logarithmic return are dynamic and time-varying,which is mainly reflected in that the skewness and kurtosis of stock return are dynamic and time-varying.Therefore,the dynamic modeling of the high-order moment of asset return has become an important research direction.In the field of dynamic time-varying high-order moments,scholars have put forward many models.One is the dynamic high-order moment modeling that directly integrates the high-order moments of yield into the model,mainly including GARCHS,GARCHK,GARCHSK,NGARCHSK,GJRSK,etc;The other is the ARCD model which indirectly controls the variables affecting the peak,thick tail and asymmetric characteristics.As an indicator of risk measurement,value at risk has attracted much attention.What kind of distribution is used to describe the probability density curve of logarithmic return will directly affect the accuracy of VaR prediction.Therefore,how to describe the dynamic characteristics of higher-order moments and establish a more appropriate probability density curve to measure VaR is also an important work.This paper improves the dynamic time-varying AR-TGARCH model in which the innovation term obeys the Gram-Charlier expansion distribution,characterizes the dynamic time-varying higher-order moments of the financial return series,and studies the prediction effect of the probability density function under the Gram-Charlier expansion distribution on VaR.In order to compare the fitting effect of the improved model on data and its ability to predict VaR,to test whether the dynamic time-varying higher-order moment has advantages over the constant higher-order moment model,and to verify whether the Gram-Charlier expansion distribution is more suitable for fitting the distribution of financial return,this paper not only estimates and compares the effects of the improved model and the improved model,but also constructs five constant higher-order moment models,They are AR(1)-TGARCH(1,1)model with normal distribution of innovation items,AR(1)-TGARCH(1,1)model with t distribution of innovation items,AR(1)-TGARCH(1,1)model with partial t distribution of innovation items,AR(1)-GARCH(1,1)model with partial t distribution of innovation items and AR(1)-EGARCH(1,1)model with partial t distribution of innovation items.The prediction effect of VaR under the corresponding distribution is tested.After research,this paper draws the following conclusions: first,it is more appropriate to choose a distribution with more peak,thick tail and asymmetric characteristics than the normal distribution to fit the residual sequence of stock logarithmic return;Secondly,the asymmetric GARCH model is better in fitting data and predicting var;Thirdly,the Gram-Charlier expansion distribution under dynamic time-varying higher-order moments has a better prediction effect on var;Fourth,the updated term coefficient of the improved dynamic time-varying higher-order moment model is larger,the fitting effect of the model is better,and the prediction of VaR is more accurate.