Risk Management Of Stock Index Fund Portfolio Based On GARCH-EVT-copula Model

With the continuous opening up of China's financial market and the continuous introduction of new financial products,financial institutions have paid more and more attention to the risk management of financial products.Stock index funds have attracted more and more capital investments due to their low transaction costs,the ability to diversify risks,and the ability to easily track the market.Many financial institutions,especially fund companies,have created many stock index fund portfolios.Therefore,risk management of stock index fund portfolios has been increasingly valued by financial institutions.Empirical research has widely found that the distribution of financial asset returns has a spike and thick tail feature.If the normal distribution is used to fit the yield data,the risk of financial assets will be underestimated.Therefore,this study will use the extreme value theory to fit the tail shape of the yield.At the same time,the copula function is used to study the joint distribution of st ock index returns in multiple countries,and to establish relationships between multiple assets,so as to better quantify the risk of investment portfolios.This article studies the risk management of an index fund portfolio consisting of the FTSE 100 Index,the Hong Kong Hang Seng Index,the S&P 500 Index,the Nikkei 225 Index and the CSI 300 Index.Considering that financial yield series with different variance,gather the characteristics of the fluctuations using GARCH model fitting return on assets,in view of the Extreme risk in financial markets,such as the financial crisis in 2008 and the 2015 stock market crash in Extreme cases,use the GARCH model fitting on standard residual error sequence and EVT(Extreme value theory)fitting super threshold condition extremum theory,Finally,combined with the copula function,the market risk of the sample fund was estimated,and the accuracy of the model was tested by Kupiec failure frequency test and independence test.Finally,by comparing the test results of GARCH-EVT-copula model with the exponential moving weighted average method,historical simulation method and GARCH correlation model,it is concluded that the Va R estimation results of GARCH-EVT-copula model at a higher confidence level are more accurate and the failure rate is the lowest.This model can better reflect the occurrence of extreme values and is closer to the real level.It is also found that the return rate of the five stock indexes deviates from the normal distribution and has the characteristics of peak and thick tail.The superthreshold condition of the data fitting with the generalized pareto distribution is better than the study based on the normal distribution.The main innovation of this paper is to use GARCH model to fit the rate of return of the constructed stock index fund portfolio while using the threshold theory and the generalized pareto distribution of extreme value theory to fit the extreme value of the data for the edge distribution,and use the copula function to link the five stock indexes.AIC and BIC laws were used to select the optimal function fitting on the distribution function of copula function and GARCH model.Finally,GARCH-EVT-copula was compared with EWMA model,historical simulation metho d and GARCH(1,1)-t model to verify whether GARCH-EVT-copula has certain advantages.