Optimization And Risk Measurement Of Portfolio Based On Copula Model

In this paper,the steps of parameter estimation and sampling simulation in the Pair-Copula Bayesian Network model are provided and represented as algorithms.We apply the vine copula model and the Pair copula Bayesian Network model to optimization and risk measurement of portfolio and compare their effects.Article introduces vine copula model to describe eight global stock market indexes during the financial crisis in 2008 and the period before and after it.Joint distribution of three periods is given in order to derive the optimal investment weights that minimize the CVaR value.Comparison of the results in the three periods shows worldwide financial crisis caused higher dependence between stock markets which has symmetry and thick tail features.Hang Seng Indexes and South Korea's KOSPI index played a key role in connecting other stock markets.Compared with C-vine and D-vine copula,R-vine copula measures the correlations of stock markets better.Based on C-Vine copula model,steps for parameter estimation and simulation in Pair Copula Bayesian Network model which is represented as algorithms can be obtained easily.Main difference between algorithms of PCBN and C-Vine is that when we loop through each node in DAG of PCBN model,identifying its parent nodes will be needed.Finally,compared with that Pair copula Bayesian Network(PCBN)model is applied to describe the joint distribution of eight global stock market indexes in 2008 during the financial crisis and periods before and after it for deriving the CVaR value and the optimal investment weights,the optimal investment weight of each asset in two models is roughly same and the CVaR value of the portfolio is very close.