ARMA-GARCH Model And The Calculation Of Var Based On Mixed Normal Distribution

The financial market is developing rapidly and more and more people have already beenor are involved in it now. However, the fluctuation in financial market is obvious to people,taking stock as an example, the ups and downs of the price make the stock market changconstantly. So people are always facing with great risk while investing in finance.VaR is theabbreviation of value at risk. VaR method which is based on risk analysis and measurement inorder to avoid risk as much as possible is currently the principle method on financial riskmeasurement. Thus the calculation of VaR actually has great realistic significance, yetweather we can calculate it exactly is still a statistical problem which is worth to study andoptimize further.The definition of VaR is the expected future maximum loss of some financial asset orportfolio within a certain period in normal market conditions and a given confidence level. Inother words, the financial asset or portfolio occurs or exceeds the value at risk only in thegiven probability level. As the definition shows, VaR method is closely related withpossibility statistics and can express the financial asset's or portfolio's maximum loss within acertain period in given possibility level using a calculated number. Although there are lots ofmethods to calculate VaR and each one has its own merits and drawbacks, yet it's still difficultto get a very accurate result, so we can only try our efforts to research constantly and considercomprehensively to reduce the error.Aming at the characteristics of kurtosis and heteroscedasticity that financial timeseries often occurs, we plan to build ARMA-GARCH Model based on mixed normaldistribution in this paper. Firstly, the characteristic and form of ARMA-GARCH Model andits identification and the parameters' estimation will be introduced, as this model is the optimal one to resolve ARCH effect. Secondly, aming at the characteristics mentioned above,we assume that the random sequence of GARCH model obeys mixed normal distribution.Although GARCH model based on normal distribution can solve heteroscedasticity to somedegree, yet it's insufficient when fitting the data which has thick tail and partial characteristics.Instead, mixed normal distribution can not only retain the advantages of normal distributionbut also solve the kurtosis characteristic and thus improve the defect that normal distributionunderestimates value at risk. Thirdly, we will get the financial asset's or portfolio's value atrisk using the function relations between itself and the VaR of random sequences in GARCHmodel which has been calculated by the definition. At last, a suitable group of stockdata(Shenzhen composite index) will be selected for empirical analysis to get a conclusionwhich proves the superiority of the method we study in this paper. Maybe the compositestructure of this newly designed method seems a little complex, yet it's very comprehensive totry efforts to reduce the errors which are usually caused in the previous models, and after theempirical analysis and comparison with others this method is proved to be reasonable andaccurate.