VaR Estimation Based On Garch-jump Family Model And Extreme Value Theory

Nowadays,the accurate simulation of asset price behavior is still an important problem in financial research.When abnormal events or shocks occur frequently,asset prices will fluctuate greatly and discontinuously.Financial market fluctuations are a kind of risk for market participants.Therefore,it is of great significance for us to select a model that can accurately describe the jump behavior of stock prices and estimate the accuracy of Value at Risk(VaR)by building a model.In the calculation of VaR,some parametric methods and non-parametric methods are often used,but these methods do not take into account the tail characteristics of return distribution.which do not take into account the tail characteristics of return rate distribution.In this paper,the GARCH-Jump model is constructed and combined with tail modeling to estimate the value at risk,so as to select the optimal model suitable for describing the Chinese stock market.First of all,after preprocessing the return rate data,it is found that the distribution of the data has the shape of sharp peak and thick tail,and there is heteroscedasticity.The basic GARCH-Jump model is constructed for them,and the maximum likelihood estimation method is used to estimate the parameters.At the same time,the extreme value theory is used to model the tail distribution of the data,and the extreme value in the sequence is constructed by selecting the appropriate high threshold value.There are two methods for the construction of extreme values: the block maximum method and the super-threshold method.Since the selection of super threshold method can take into account all data of return rate at the same time,the POT model of super threshold method is adopted in this paper to describe tail behavior.The GARCH-Jump model and POT model are combined to calculate the daily value-at-risk(VaR),and the model fitting is judged according to the failure rate of VaR estimation.In the empirical study,three indexes are selected: CSI 300 index,Gem 300 index and Hang Seng Index.At different significance levels,the generalized Pareto distribution(GPD)is used to construct the calculation formula of VaR,and the calculated results are compared.It is found that the fitting effect of the ARJI-GARCHJump model was the best.Meanwhile,In order to show the important role of extreme value theory in risk management,VaR was calculated by ordinary parameter method and compared with the above results,indicating that the addition of POT model improved the accuracy of VaR estimation.