Multivariate GARCH Model And Its Application In VaR

In this article, the author concerned with a better description of the volatility and correlations under multivariate GARCH model compared with univariate GARCH model. Which means when the first moment or the second moment of the time series affects mutually, the multivariate GARCH model can include this kind of influence to the model, therefore enhances the precision of the GARCH model and other financial models that based on the volatility.First of all, the author discusses the extension from univariate GARCH to multivariate GARCH model and the important role of the MGARCH model in the modern financial research. Especially in recent years, as the word trend economic integration intensifies, there is a significant increasing in the co-movement of the world's financial markets. Through multivariate GARCH model we can seize this co-movement and therefore MGARCH is a better tool to describe the volatilities among several markets. This paper presents several important MGARCH model: VEC model, the constant correlation MGARCH model, BEKK model, Cholesky decomposition method and the characteristics and limitations of each. In the later part of the paper we established 3-variable BEKK model and Cholesky decomposition model including three exchange rates: Euros, Canadian dollars, pound sterling and focus on the time-varying correlation coefficient. In the part of the calculation of VaR, we illustrate the application of MGARCH models by considering the VaR of a financial position with three assets. The calculations of the variance and correlation coefficients are based on two ways: First, univariate GARCH model and constant correlation coefficients and the alternative way is through MGARCH model. We also make a comparison of the VaR performance of them, and find that VaR based on the MGARCH model always have a better performance than based on the univariate GARCH model. The article also discussed a series of deficiencies in the concluding part.