Risk Measure Based on ARMA-TGARCH-GED-Copula Model

- Financial return series often show the characteristics of peak and thick tail, bias, and volatility aggregation effect. In this paper, ARMA-TGARCH is introduced to model each asset return series, the standard residual term of which is assumed to obey the generalized error distribution (GED). The joint distribution model with a multivariate copula function is used to characterize the dependence structure between high-dimensional asset variables. Combining the Monte Carlo simulation method, the return series of each asset is generated, and the VaR and CVaR of portfolio investment are calculated. The empirical research shows that there is obvious autocorrelation, heteroscedasticity effect, and asymmetric volatility in the return series of the representative stock indexes of China and the United States, which is suitable for ARMA-TGARCH-GED to fit marginal distribution. The failure frequency test of VaR prediction proves that ARMA-TGARCH-GED-Copula model can be better applied to the risk measure of portfolio investment.