The Analysis Of VaR Of A Stock Portfolio Based On Vine Copula-GARCH Model

With increasing economic globalization, the world-wild capital markets have also been closely linked together, the volatility of one of the world’s major capital markets will often trigger a chain reaction around the world. In order to respond to these adverse impacts of volatilities in a more positive way, it is very urgent and important for us study the increasingly close relations among the world’s major capital markets.Flexible multivariate distributions are needed in many areas, not just in Economic and Financial. The popular multivariate Gaussian distribution is however very restrictive and cannot account for features like asymmetry and heavy tails. Therefore dependence modeling using copulas is nowadays very common to account for such patterns. The use of copulas is however challenging in higher dimensions, where standard multivariate copulas suffer from rather inflexible structures. Vine copulas overcome such limitations and are able to model complex dependency patterns by benefiting from the rich variety of bivariate copulas as building blocks.Vine copula function allows us to build complex multivariate joint distribution function step by step, started by studying the marginal distribution of simple univariate functions. And the correlation between the variables obtained under the built multivariate joint distribution function, is not a simple linear relationship, but the non-linear relationship which is more practical.Establishing a good multivariate joint distribution function contains a few factors as follow:to select the right vine structure during the process of building the multivariate joint distribution model by pair-copulas as building blocks; to select the most fitted copula type for each pair-copula among the a variety of copulas family; the most important thing is to deal with the marginal distributions of all the variables carefully.In terms of background knowledge of this paper, we first introduce the properties and the application of the general copula function,the idea of the vine copula and the details of constructing the multivariate copula function.Then we illustrate the properties, the application and test method of the ARMA model and the GARCH model,which is always used to deal with time series.Then combining the above knowledge, we study the of rates of return between the international mainstream stock markets,and also the relationship of rate volatilities between them.When dealing with marginal distributions of the variables,we take the process of dealing with rate of return of the Shanghai Composite Index for example.This article is intended to view the return series as either time series or time-independent random sequence, and study them respectively.When the return series are considered as time series, we found the time series are correlation and heteroscedasticity. To eliminate the effect of correlation and heteroscedasticity,we built up the most suitable ARMA (2,2)-GARCH (1,1) model step by step.Since the fact that the residual series filtered by ARMA (2,2)-GARCH (1,1) model can still not meet the original hypothesis,which assumed the filtered residual series meet standard normal distribution,it is impossible to fit the filtered residual series with the normal marginal distribution.Then we have to use its empirical distribution function to deal with its marginal distribution, after that,the issue we studied has transformed from the relationships between rates of return to the relationship between return volatilities.while we see the return series as time-independent random sequence,we directly use its empirical distribution function to deal with this random sequence,and the issue will remain the same.After dealing with all the varieties’marginal distributions, we use C-vine structure and D-vine structure to construct multivariate copula function of the return rates and the return volatilities respectively,comparing the parameters estimated in the division with the parameters estimated in the overall,comparing the parameters estimated under the C-vine structure with the parameters estimated under the D-vine structure,and comparing all the goodness of fit.We also analysis the relations among the world’s major capital markets by the relations of their return rates and return volatilities,Finally,base on the multivariate joint distribution function we built,we use Monte Carlo simulation and VaR model to analysis the portfolio of stocks.