Extreme VaR Measure Based On ARMA-GARCH Family-M-EVT Models

Nowadays,the extreme risk of the financial system is closely related to the economic development.Once the prevention and control of the extreme risk of the financial system fails,it will lead to the financial crisis in the country and even in the international scopes.Therefore,it's of great significance for economic development to control the extreme risk in financial markets effectively.This paper mainly studies the prediction ability of ARMA-GARCH family-M-EVT mod-els to the extreme risk.In order to predict the extreme risk of return sequence of financial asset-s,the heteroscedasticity and risk premium of return sequence are treated by ARMA-GARCH family-M-EVT models.Combining the advantages of EVT method to capture the thick tail of return sequence distribution.Models are proposed to deal with the heteroscedasticity,risk pre-mium and distribution of peak return and thick tail simultaneously-ARMA-GARCH family-M-EVT models.Finally,this paper selects stock data of AAPL and MSFT as the research ob-jects and uses proposed models to fit that stock's return series.The results show that the model considering the risk premium characteristics is better than the model without considering the characteristics of the risk.