Realized GARCH Model Based On Extreme Value Theory And Its Application In Risk Measurement

With the continuous progress of economic globalization,China’s potential financial risks are gradually released.The violent turbulence in China’s stock market in 2018 has sounded an alarm for people to fend off risk in the stock market.In addition,in recent years,with the rapid development of margin trading and stock index futures trading,the leverage of China’s securiti’es market has been increasing,and its intraday volatility has increased significantly.In the stage of market fluctuation,the extreme value characteristics of index return become very important.More and more fund companies also use index products as performance evaluation comparison,and market volatility has significant uncertainty for both practitioners and investors.Therefore,it is very important to manage the uncertainty of the index in the market fluctuation stage,especially the extreme risk management.At present,VaR model is the most popular risk measurement tool in the world.Because of the inherent defects of VaR,ES is gradually applied to risk measurement by more and more scholars to achieve better measurement effect.Therefore,this paper uses VaR and ES as risk measurement indicators.For the calculation of VaR and ES,firstly,the Realized GARCH model is introduced,and its residual is extended to the case of thick tail to characterize the characteristics of financial time series,such as peak thick tail,volatility aggregation,and compared with the traditional GARCH model.Secondly,considering the extreme phenomena of stock data soaring and falling,the extreme value theory is introduced to model the small probability extreme events,and the POT model is used to study the tail risk characteristics of the series.Finally,in order to improve the accuracy of describing extreme risk,this paper combined the POT model and the Realized GARCH model to construct the Realized GARCH-EVT model and then compared with GARCH-EVT model,Realized GARCH model and POT model.In the empirical research,this paper selects the Shanghai composite index and Shenzhen Component Index from January 4,2005 to February 28,2008,and tests the fitting effect of the model with the likelihood function,as well as using failure rate,unconditional coverage test,independence test,mixed test,error efficiency and mean square error to compare effect of model in VaR and ES under Backtesing.The empirical results show that:compared with GARCH model,Realized GARCH model has better performance of fitting and risk measurement;at a higher level of confidence,the extreme value theory POT model can better describe the tail shape of distribution,improve the accuracy and effectiveness of the model;combine Realized GARCH model with extreme value theory to construct the Realized GARCH-EVT model can achieve more accurate measurement of extreme risk.