| For high-dimensional financial data,the classical multivariate normal distribution cannot describe their dependency structure well.Especially when extreme events occur,the stock indexes of various countries in the world will change significantly and synchronously.In order to flexibly describe the correlation between variables,the Copula method has gradually received attention.The advantage of the Copula method is that the joint distribution between variables can be disassembled into marginal distributions and a Copula function,allowing one to focus on the correlation between variables and use the more abundant Copula functions to characterize the dependency structure and establish a joint distribution.However,many studies on Copula have focused on two-dimensional situations or multi-dimensional Copula with the same structure.For a complex subject,requiring all the variables to have the same correlation structure is unrealistic,and it also obliterates the advantages of Copula method on flexibly fitting the data.An important extension is Vine Copula.Vine Copula’s special feature is that starting from the conditional distribution of variables,different two-dimensional Copula and different parameters are allowed to fit the microstructures of the two variables,inheriting the advantages of the Copula function.This thesis conducts modeling and testing based on the data from the stock indexes of the eight major economies in the world from 1998 to 2018.First,the marginal distribution of the stock index was fitted using the GJR-GARCH(1,1)model with no constant term in the volatility equation.Secondly,the C-Vine Copula and D-Vine Copula models were established between eight markets using five commonly used binary Copula as alternative local structures.Subsequently,we used the two Vine Copula models to calculate the VaRs(Value at Risk)for the global stock index portfolio using the Monte Carlo method.Finally,we performed backtesting for VaRs with confidence levels of 0.99,0.975,0.95,and 0.9 calculated by different models.This thesis features an empirical research section and has obtained some achievements.The first is to apply the Vine Copula method to stock indexes of eight major economies including China,using the data of nearly 20 years,which is larger than other scholars do.The second is to use the established Vine Copula model in combination with Monte Carlo simulations to calculate the VaRs of the stock index portfolio outside the sample for one year and to test and plot it,validating the excellent performance of the Vine Copula model in the field of VaR calculation.The third is the observation that C-Vine Copula is more accurate than D-Vine Copula. |
