Risk Measurement Of Implemented GARCH Model Based On GLDI Distribution

With the development of data storage technology,using high-frequency data to model volatility has become an important research direction of financial market.In the early stage,the modeling of high-frequency data generally assumed that the financial time series obeyed the normal distribution,but the actual financial data presented the phenomenon of ‘peak thick tail',so this paper extended the Realized-GARCH to the case that the error term obeyed the peak thick tail distribution.Randomly select a stock in three different industries,respectively,use normal distribution,traditional skew logistic distribution and GLDI distribution to fit the density function of the real logarithm yield of the three stocks,and preliminarily understand the phenomenon of ‘peak and thick tail' of financial data through graphs.Then through the kurtosis test,skewness test,K-S normal test,K-S GLDI test four kinds of statistical hypothesis test to further understand the actual distribution of the logarithm yield of the three stocks.By comparison,the real logarithmic returns of the three stocks do not conform to the normal distribution,and the actual distribution shows the phenomenon of peak thick tail and skewness.The traditional skew logistic distribution and GLDI distribution fit the actual distribution better than the normal distribution.However,the traditional biased logistic distribution is not conducive to data analysis because the variance and expectation are not explicit form.Intuitively,selecting GLDI distribution can better fit the characteristics of peak,thick tail and skew of actual data.Different from the traditional skew logistic distribution,the skew degree of the distribution is directly controlled by the skew coefficient.GLDI distribution can control the skew degree of the distribution by controlling the shape parameters.In this paper,the Realized-GARCH(1,1)model is selected.When the error distribution obeys the GLDI distribution and the expectation of the leverage function is 0,the leverage function is modified appropriately,and the maximum likelihood estimation method of the model is given.Based on the five minute trading data of Shanghai Securities Composite Index and Shenzhen Securities Component Indexfrom September 16,2017 to December 19,2019,the Realized-GARCH(1,1)model with the error term following the standard normal distribution and the Realized-GARCH(1,1)model with the error term following the GLDI distribution(Type I generalized logistic distribution)are established respectively.QMLE(quasi maximum likelihood estimation)is used to estimate the parameters of the two models by R software,and then VaR prediction is carried out by using the method of out of sample prediction.The 556 day data after processing is divided into two parts.The first 456 day sample is used to estimate the Realized-GARCH model,and then 100 data out of the sample are predicted by the estimated model.Then,using Kupiec failure rate test method and LR(maximum likelihood estimator)to compare the failure rates of the two models under different confidence levels.The results show that the GLDI model,which extends the error term to the peak and thick tail distribution,can measure the return risk of Shanghai Securities Composite Index and Shenzhen Securities Component Index more accurately than the model whose error term follows the standard normal distribution,and can vividly describe the leverage effect of the price fluctuation of Shanghai Securities Composite Index and Shenzhen Securities Component Index.