An Improved Vine Copula Model And Its Application In Financial Risk Measurement

With the development of the financial market,the research of financial risk measurement is particularly important.To solve the problem of risk measurement for financial data,Vine Copula-Va R model came into being.Vine Copula model used the principle of the sum of the absolute values for Kendall’s rank correlation coefficient to construct the maximum spanning tree to complete the vine structure model,while the rank correlation coefficient can only describe the one-sided collaborative relationship among variables,Considering the advantages of mutual information in describing the interaction among variables,this paper proposes to construct the Copula function model of C and D vines based on the maximum spanning tree based on mutual information theory and apply them to the financial risk measurement.In this paper,we used mutual information method to construct the C and D vine Copula models of the daxreturns data set through R language Vine Copula package,and compare the goodness fit through Monte Carlo simulation.Compared with the corresponding models based on Kendall’s rank correlation method,the outperforms of the C and D copula models constructed by the mutual information method can well fit the original data.The risk measurement of the 23 US stocks was studied by using the rattan Copula-Va R model based on mutual information.The normalized residual of each yield was obtained by fitting the ARMA(1,1)-GARCH(1,1)model.The normalized residual series were established by using the C rattan and D Vine Copula models based on mutual information.The results showed that Compared with the C and D vine structures based on Kendall coefficient,the C and D vine structures based on mutual information have been changed,and different vine structures have been generated.Finally,the time rolling risk prediction with an interval of 1 day has been carried out for the four models.Although all of them have passed the non-conditional coverage backtest test and conditional coverage back-test test of Va R,the results showed that compared with the traditional C and D Vine Copula-Va R,The Copula-Va R model of C and D vines based on mutual information method was proposed to achieve better risk measurement effect.The innovations of this paper are as follows:1.Based on the concepts of mutual information and joint entropy,the mutual information ratio and conditional mutual information ratio between two random variables are defined to indicate the impact of the information interaction between variables on the information contained in the whole;2.Based on this index,the calculation process for the establishment of the C vine and D vine Copula models is updated.The C vine and D vine Copula models constructed by this method have more robust characteristics than the traditional C vine and D vine Copula models.