Multivariate Time-Varying G-H Copula GARCH Model and Its Application in the Financial Market Risk Measurement

Abstract

Taking full advantage of the strengths of G - H distribution, Copula function, and GARCH model in depicting the return distribution of financial asset, we construct the multivariate time-varying G - H Copula GARCH model which can comprehensively describe "asymmetric, leptokurtic, and heavy-tail" characteristics, the time-varying volatility characteristics, and the extreme-tail dependence characteristics of financial asset return. Based on the conditional maximum likelihood estimator and IFM method, we propose the estimation algorithm of model parameters. Using the quantile function and simulation method, we propose the calculation algorithm of VaR on the basis of this model. To apply this model on studying a real financial market risk, we select the SSCI (China), HSI (Hong Kong, China), TAIEX (Taiwan, China), and SP500 (USA) from January 3, 2000, to June 18, 2010, as the samples to estimate the model parameters and to measure the VaRs of various index risk portfolios under different confidence levels empirically. The results of the application example are in line with the actual situation and the risk diversification theory of portfolio. To a certain extent, these results also justify the feasibility and effectiveness of the multivariate time-varying G - H Copula GARCH model in depicting the return distribution of financial assets.