Application Of GARCH Models And G-VaR In Risk Measurement

With the continuous expansion of financial markets at home and abroad,financial participants and financial researchers pay more and more attention to the risk measurement and risk management of various financial markets.China’s financial market is now developing stronger,the risk control can not be ignored,and the risk management level of each market should also be continuously improved.At present,the main method of risk measurement is value at risk(VaR).Var can not only measure the risk of a single stock or fund,but also measure the market risk of more complex portfolio.It is a more comprehensive market risk measurement tool.This paper uses VaR method to measure risk.Generally,in risk measurement,it is often assumed that the yield of financial time series obeys the normal distribution,while the actual financial time data often has the characteristics of peak and thick tail.The assumption based on the normal distribution will underestimate the risk.At the same time,VaR pays attention to the loss of the lower tail.As an effective method to measure extreme events,extreme value theory can capture the tail characteristics of data distribution and help to measure the tail risk under extreme events.In addition,nonlinear expectation theory is put forward on the problem of model uncertainty,which can be more in line with practical problems.This paper attempts to apply the G-normal distribution in the sublinear expectation space to the processing of financial data,establish GARCH-G-VaR model,and explore the application effect of this model in risk measurement.This paper takes China’s industry index as the research object,selects the four industry indexes in the CSI industry index as the research sample,and explores the risk of the four industry indexes.Using the daily closing price data of four industry indexes to calculate the daily logarithmic yield series,carry out a series of tests on the yield series,and model according to the test results.In the modeling stage,this paper uses GARCH model modeling.After establishing GARCH model,the model is tested for parameter significance and arch test to ensure the effectiveness of the model.After selecting the appropriate model,the VaR values of the four industry indexes are estimated based on each model.In addition,considering the influence of extreme events in the process of measuring risk,the extreme value theory is introduced to describe the tail shape of the return series distribution of four industry indexes.The application method is the pot model commonly used in extreme value theory and GARCH-EVT model is established in combination with GARCH.At the same time,considering the uncertainty of the residual distribution after using GARCH model,it is assumed to be G-normal distribution in sublinear expectation space,and GARCH-G-VaR is calculated.In order to evaluate the effect of risk measurement,GARCH model,GARCH-EVT model and GARCH-G-VaR model are compared and analyzed at 95%and 99%confidence levels,and the accuracy of the estimated VaR value is tested in combination with kupiec failure rate test.The empirical results show that when the confidence level is 95%,the gap between the effect of VaR estimated by GARCH-EVT model and that estimated by GARCH model is not obvious.When evaluating the index risk of different industries,the models have their own advantages and disadvantages.Compared with the other two models,GARCH-G-VaR model is more conservative in the calculation of VaR at the 95%confidence level.When the confidence level is 99%,GARCH-G-VaR model and GARCH-EVT model can accurately estimate the VaR value for the four industry indexes.In comparison,the effect of GARCH-G-VaR model is better than GARCH-EVT model.This shows that under a high confidence level,GARCH-G-VaR model has a good effect in the application of risk measurement.