Application of copula and Copula-CVaR in the Multivariate portfolio optimization

In this article we resort to the copula theory and CVaR measures in the portfolio management, using copula function and copula-CVaR to design the portfolio optimization. We initially apply the three-dimensional Archimedean copula in the empirical study. After estimating the multi-dimensional copula, we use Monte Carlo method to generate the scenarios for the calculation of portfolio's variance and CVaR. Then we apply the minimum of copula based standard variance and CVaR as the objective function of the portfolio programming. The multivariate demonstration indicates that the copula theory and copula based CVaR method does better in the portfolio management than the normal hypothesis.