Improvement Of Garch-Jump Model Based On Over-Discrete Features

The dynamics of financial asset prices and their volatility models have been important research topics in academia and industry.Because the existing GARCH-Jump model has a deficiency in the setting of the number of jumps obeying the distribution,it is difficult to describe the agglomeration characteristics and over-discrete characteristics of jumps,which makes it impossible for the model to more accurately fit the movement behavior of financial markets with sudden events.Therefore,it is of great significance to construct a GARCH-Jump model capable of characterizing the jumping over discrete features.In the original GARCH-Jump model setting,it is assumed that the number of jumps obeys the Poisson distribution.The characteristics of the Poisson distribution make it impossible to characterize discrete features,and the negative binomial distribution(NB)can do this well.One point,because it has more variance than the expected statistical characteristics.Therefore,this paper has established the NB-GARCH-Jump model with discrete features and discussed the statistical characteristics of the newly established model.At the same time,two new estimation methods of the new model are proposed,including maximum likelihood estimation and Bayesian estimation based on Markov chain Monte Carlo(MCMC)method.The newly established model and the original GARCH-Jump model are calculated using the DIC index.The comparison is made and the validity of the NB-GARCH-Jump model is illustrated.First,based on the Poisson-Gamma mixed distribution method,this paper constructs a NB-GARCH-Jump model that can characterize the agglomeration of jumps.That is,based on the Poisson distribution,the prior information is added to make the parameters of the Poisson distribution obey the Gamma distribution.The posterior negative binomial distribution is obtained;further,by considering the variance information of the number of jumps,a time-varying equation of the jump intensity is constructed,thereby obtaining a NB-ARJI-GARCH model with time-varying characteristics.Based on the completion of the model construction,the high-order moments of the NB-GARCH-Jump model and the GARCH-Jump model are calculated,which proves the advantage of the NB-GARCH-Jump model in characterizing the characteristics of the peak and thick tail of financial asset returns.Secondly,the differences between the NB-GARCH-Jump model and the GARCH-Jump model in the volatility and return rate are studied using simulation methods.The transmission mechanism of the jump term in the NB-GARCH-Jump model is explained.The negative binomial jump It makes the volatility exceed the kurtosis,and the volatility makes the yield exceed the kurtosis.It also shows that the negative binomial jump has the advantage of describing the agglomeration of the jump.The MCMC method was used to simulate the two models,and it was found that the NB-GARCH-Jump model has smaller estimation errors and smaller DIC.At the same time,the estimation of discrete parameters is more accurate.The estimated values of all parameters are in 95 The% confidence interval indicates the effectiveness of using the NB-GARCJH-Jump model.Finally,the empirical study of the SME index,the CSI 300 index,the Dow Jones index,and the S & P SME index,found that the logarithmic return series of the four indices are all non-white noise series with left-biased,spike-thick tails.Characteristics,fluctuations up and down significantly.The GARCH-Jump model and the NB-GARCH-Jump model were used to estimate these four indices through the MCMC method.When the model converges,the results show that the NB-GARCH-Jump model can estimate and fit the GARCH-Jump model on all four indices.Discrete parameters that cannot be estimated,and the former are better than the latter,which provides a certain reference value for financial investment and risk management.