Research On ES Prediction Of Chinese Stock Market Based On FZ-GAS-RS Model

Basel III requires that Expected Shortfall(ES)replace Value at Risk(VaR)as a risk measure of market risk capital.Although ES is Coherence,ES is not Ellicitability,so the accuracy of the posterior ES measurement model cannot be obtained.Fissler and Ziegel(2016)proposed the FZ loss function to prove that ES and VaR can be jointly induced.Patton et al.(2019)proposed a generalized autoregressive score(GAS)model based on FZ loss function for joint estimation of VaR and ES.The model does not need to assume the distribution and dynamic process of the yield series,and its prediction performance is significantly better than the parametric and nonparametric models.In this paper,Realized Skewness(RS)is introduced into Patton et al.(2019)model to obtain more information to estimate the tail risk of financial market,and whether the introduction of RS can improve the ES prediction performance of FZ-GAS model is studied.Realized skewness,as a higher-order moment,can measure stock investment returns,volatility and risk,and contains external information in the stock market,such as the asymmetry of volatility,heterogeneous beliefs and short selling restrictions,and overreaction to good news.Allen et al.(2012)revealed the strong predictive power of financial skewness on future economic conditions.Amaya et al.(2015)calculated RS using daily frequency data,and found that RS can significantly affect the future yield of stocks.Mei et al.(2017)proved that RS can significantly improve the accuracy of medium-term and long-term volatility prediction in the stock market.Based on joint scoring function and combined prediction of VaR and ES,this paper incorporates the realized skewness into the FZ-GAS model for the first time,and constructs the FZ-GAS-RS model to jointly predict VaR and ES.The 5-minute closing prices of the Shanghai Composite Index and the Shenzhen Component Index from January 1,2005 to November 30,2022 were selected.Through in-sample parameter estimation and out-of-sample prediction,combined with goodness-of-fit test,DQ test,DES test and DM test,the prediction performance between the rolling window model,the FZ-GAS model and the FZ-GAS-RS model was evaluated to verify whether the inclusion of RS into the FZ-GAS model can improve the VaR and ES accuracy of the model.Empirical research shows that: First,on the whole,the FZ-GAS-RS model can predict the ES value in time and accurately,and the introduction of RS into the FZ-GAS model can improve the prediction performance of the model.Second,for a single model,the GAS-GARCH-RS model in the FZ-GAS-RS model is more accurate for ES prediction,which can better fit the out-of-sample data,provide investors with accurate tail risk information in time,and reduce the possibility of investors suffering losses due to underestimating risks.