Analysis Of Portfolio Using Multivariate Copula Bayesian Stochastic Volatility Models

With the continuous perfection and development of financial markets and financial system of China, more and more people and institutions have began to join in the stock market. However, Investment is always companied by risk. Ever since Henry Markowitz established the portfolio theory in1952, it has been realized that the diversified portfolio is beneficial to reduce risk. Since then, many scholars have conducted related research and achived many meaningful results.With the In-depth study of financial time series, scholars have found that the classical portfolio theory is deficient to depict the statistical characters of the rate of return of financial assets. on the one hand, the rate of return of financial assets don’t follow normal distribution, usually they have higher kurtosis and thicker tails and the volatility of rate of return is time-varying and aggregated, sometimes it behaves "leverage effect"; on the other hand, there is not only linear relationship but also nonlinear relationship among the rate of return of financial assets. For this reason, we choose the stochastic volatility models that have an advantage to describe the fluctuation of Financial assets and the Copula function which is good at measuring the correlation among financial assets to study this problem.In the first place, this paper gives an relatively comprehensive review to stochastic volatility theory and Copula functions and the theory of risk measurement of financial markets. on this basis, we use the leverage SV-t models to model the marginal distributions of fiancial assets and we use copula function to describe the correlation among financial assets, then we construct the multivariate Copula leverage SV-t models. In empirical research, we choose three industry indices in the Shenzhen stock market as our reserch objects. Firstly, we use the leverage SV-t model to model each of the three industry indices’rate of return, then we fit the data of rate of return to several different Copula functions to obtain the best fitting Copula function. By using the best fitting Copula function we construct the corresponding multivariate Copula leverage SV-t models to reflect the portfolio’s joint distribution function. At last, by using the Markov Chains Monte Carlo simulation methods, we calculate the portfolio’s value at risk(VaR) and conditional value at risk(CVaR) at different confidence levels, further more we give the correspondiong optimal invesment ratios. The empirical research indicates that the model we have constructed is effective. It can provide guidence to investors and help investors to disperse and control the overall portfolio risk.