The Application Of Two-parameter Copula Function In Tail Dependence Analysis Of Financial Risk

The tail-dependent relationship between financial assets,that is,the same increase and fall is the object of concern to investors.This paper uses the two-parameter Copula function to describe the tail-dependent behavior of financial assets,and applies it to the actual situation to study the tail-dependent relationship between the Chinese and American trade disputes before and after the Shanghai Composite Index's return rate and ZTE's return rate.It overcomes the shortcomings of the single-parameter Copula to describe the financial tail dependence,and better describes the tail-dependent relationship between ZTE and the Shanghai Composite Index before and after the trade dispute.Firstly,this paper chose the two-parameter BB1 and BB7 Copula functions for research.We derive these two two-parameter log-likelihood function estimators,use the maximum likelihood method to estimate the parameters of the model,and find the expressions of the upper and lower tail-dependent coefficients;make their density function image and contour image,It can be seen that these two two-parameter Copula functions are suitable for describing the tail data;we generate random numbers under different parameters,simulate the maximum likelihood estimation,find that the maximum likelihood estimation can effectively estimate the parameters,and increase the sample size,The estimation accuracy of the parameters is further improved.Secondly,the application of the two-parameter Copula function.The trade dispute between China and the United States not only affected the trend of China's securities market,but also caused serious losses in stocks with a large relationship with disputes.This paper uses the two-parameter Copula function to describe the tail-dependent behavior of ZTE and Shanghai Composite Index before and after the trade dispute.(1)We collected the closing price data of ZTE and Shanghai Composite Index from July 28,2015 to January 4,2019,except for the trading day and the suspension date,and selected the trading days of both,Statistics of their logarithmic rate of return characteristics,make their income graphs find that the rate of return sequence has an aggregation phenomenon;on March 23,2018,as the node of the trade dispute between China and the United States,the statistical characteristics of the rate of return before and after the trade dispute are statistically analyzed.(2)Construct a time series model to describe the return sequence and describe the risk characteristics from the perspective of risk at value.The stationarity test and ARCH effect test are carried out on the rate of return series.The results show that the sequence is stable and there are conditional heteroscedasticity.GARCH model is established for sequences under the assumption that the residuals follow normal,t-distribution and generalized error distributions.After repeated comparative analysis,the optimal model was selected to calculate the VaR with 95% and 99% confidence level.The VaR image was obtained and the failure rate of VaR was tested.The results show that the models can effectively estimate the risk at value.(3)Construct a two-parameter Copula function to describe the tail-dependent behavior of ZTE and the Shanghai Composite Index We made a non-parametric estimate of the distribution of the Shanghai Composite Index and ZTE before and after the trade dispute.Estimates show that trade disputes have a greater impact on them.Using the traditional linear Pearson correlation coefficient to analyze the correlation before and after the trade dispute,the results show that the Shanghai Composite Index and ZTE have a greater correlation before the trade dispute,and the correlation between the two stocks is smaller after the trade dispute.We estimate the parameters of the two-parameter BB1 and BB7 Copula,and use the AIC criterion to judge the effect of the fit.The results show that the fitting effect of the two-parameter BB7 Copula function is better than the fitting of the two-parameter BB1 Copula function.Select the two-parameter BB7 Copula function as a function to characterize the correlation between the Shanghai Composite Index and ZTE.According to the calculation formula of the tail dependence coefficient,the dependence coefficients of the upper tail and the lower tail before and after the dispute are calculated.The result is still the Shanghai Composite Index and ZTE has a smaller coefficient of dependence after the trade dispute,which indicates that the risk of ZTE is not caused by the Shanghai Composite Index,but the impact of trade disputes on ZTE,and its impact is greater than the impact on the Shanghai Composite Index.Therefore,the tail dependence coefficient better reflects the risk of financial assets.This paper provides a new method for investors analyze the behavior of financial assets tail dependence.