ES Model And Empirical Analysis Under Sublinear Expectation

In recent years,due to the impact of the COVID-19 pandemic and the downward economic cycle,global inflation has continued and the road to economic recovery has been long and difficult.In the context of global economic and financial integration,risk management is particularly important,and risk measure,as the basis and key of risk management,has naturally become the focus of individual investors and financial institutions.At present,the mainstream risk measures in the financial market are VaR and ES,which are the unified standards for financial regulatory agencies to measure risk.Since ES takes into account the occurrence of extreme cases based on VaR and satisfies the properties of coherent measure of risk,it has received a lot of attention from the academic community since it was proposed,and various kinds of application studies have emerged.As an important theory of nonlinear expectation,sublineax expectation can better describe distribution uncertainty compared with linear expectation in traditional probability theory axiom system.Therefore,this paper conducts a study under the framework of sublinear expectation,assuming that the return rate of financial assets follows a G-normal distribution,and proposes a new risk measure G-ES model based on G-VaR model,which innovatively gives its discretization definition and calculation method,and discusses GES in the limit form as the theoretical support for the definition of discretization.This calculation method takes into account the dependence of the estimation window on the significance level,and can be well combined with G-VaR model for multinomial backtesting.In addition,based on the Christoffensen test,an independence test applicable to G-ES is proposed,considering the characteristics of the discretization calculation method.Based on the G-VaR model and the G-VaR*model after adding the autoregressive model,combined with the discretization definition of G-ES,this paper presents the specific algorithm for the G-ES model and the G-ES*model,and combines the CSI 300 Index,the Hang Seng Index,the S&P 500 Index and the FTSE 100 Index for empirical analysis to explore the performance of each market under different estimation windows and different discretization segments.For G-ES model,it can obtain better conditional coverage test results under different widths of historical data windows.The analysis shows that larger estimation windows can capture the long time average losses,while smaller estimation windows can capture local changes in returns,which is closer to the real situation.Considering the complexity of adjusting the estimation window and the backtesting results,it is believed that the G-ES model performs better when the number of discretization segments is 4.For G-ES*model,its conditional coverage test and independence test are better than G-ES,with higher accuracy and independence,and the window adjustment operation is easier,with better robustness and applicability in different markets.Compared with normal distribution method,historical simulation method,POT model and dynamic AR(1)-GARCH(1,1)model,both G-ES model and G-ES*model have significant advantages under different estimation windows.