Analysis Of Portfolio VaR Pair Copula-LMSV-t

In recent years, influenced by globalization deepening, financial innovation and technological progress, the China’s capital market, especially the stock market, has more prominent characteristics than ever before in terms of volatility, complexity, nonlinearity and uncertainty. Therefore, the general investors, represented by the social security fund, need to have a stronger ability of risk prevention. According to the modern portfolio theory, diversified portfolio provides convenience to eliminate the non-systemic risk. Thus, in practice, portfolio is widely used by institutional investors. Portfolio management is the core content of investment decisions.Here the LMSV-t model is adopted to estimate the marginal distribution, instead of the GARCH model, which has been adopted before, and the pair copula-LMSV-t model is constructed. Furthermore, the method of parameter estimation of LMSV-t by MCMC is offered. The LMSV-t model is more superior in describing the volatility clustering, high peak, thick tail, and long memory of asset’s return.An empirical example with the social security fund’s five holdings is offered, which from January1,2012to December31,2013. Firstly, the basic statistics of the sample showed that each asset’s return has many characteristics, such as volatility clustering, high peak, thick tail, and long memory et al. The LMSV-t was used in modeling the marginal distribution and has a very good performance in the parameter estimation and goodness-of-fit test of the DIC criterion. Then, after determining the nodes and selecting suitable binary copulas, the pair copula method was used to construct the high dimensional dependency structure. Lastly, the portfolio’s VaR was got and used for the kupeic’s test.Apparently, by using the LMSV-t model as the description of the marginal distribution, the pair copula-LMSV-t model has a better performance in describing the nonlinear characteristics of each asset and the dependency between assets.