Multivariate Financial Asset Portfolio Risk Value Measurement Based On The Theory Of Copula

Financial yield on assets not only has sharp-peaks, fat-tails, heteroscedasticity,but also has long memory. So the paper combines the theory of Copula with ARFIMA-GARCH model to measure multivariate financial assets portfolio risk value.The paper establishes the ARFIMA-GARCH-Copula model for financial portfolio, which is composed by Shanghai Stock Index yield and Shenzhen Component Index yield equal weight to research the related structure and risk value of VaR. First R/S analysis is adopted to test the long memory of a single asset.Second, choose different GARCH models to fit each asset return series. Third, select Copula function to describe the relational structure between each asset. Fourth, use Monte Carlo method to produce each return sequence of the assets to calculate VaR of the portfolio. The empirical analytical results show that there is apparent long memory property in the Shanghai and Shenzhen stock market which has symmetrical tail correlation. Kupiec test results show that the model of ARFIMA-GARCH-Copula is more efficiency than GARCH-Copula model in measure the portfolio risk.Considering three financial assets portfolio, two financial assets subject to Copula function is not necessarily the same. So the paper combines Pair Copula which describes the structure of multivariate random variables and ARFIMA-GARCH model to establish ARFIMA-GARCH-Pair-Copula model to calculate VaR of the portfolio which is composed by Shanghai Stock Index yield, Shenzhen Component Index yield and Hongkong Hengsheng Index yield. The ARFIMA-GARCH model describe the volatility of the yield on assets. The paper selects the master node according to the correlation between variables strength. And it choose the right Pair Copula function through scatter plot among the variables. The model not only considers the assets yield of long memory, heteroscedasticity, but also captures the correlation among the portfolio to describe the joint distribution of the portfolio and calculate risk value VaR. The empirical analytical results show that compared with multivariate Normal-Copula, multivariate t-Copula method of VaR model, Pair-Copula-ARFIMA-GARCH model describes the high-dimensional related structure more flexible. And compared with the zero order difference and first order difference, the VaR calculation of return with fractional order difference is the most close to the risk value calculated by Variance-Covariance.