Application of Multivariate GARCH Models to Assets Joint Volatility and Return Estimation

This study proposes parametric and semi-nonparametric adaptations of the asymmetric EGARCH model to the multivariate case using the DCC-GARCH parametrization framework. The developed methods allow to model the joint dynamics of the conditional volatility of several assets accounting for the stylized fact about the asymmetric relationship between volatility and shocks in returns. The presented semi-nonparametric generalization of both univariate and multivariate EGARCH processes provides a more flexible estimation procedure by relaxing the assumption of a normality of shocks. The implementation of this approach is based on the adaptation of the Gallant and Nychka density approximation method to the family of GARCH models. In the multivariate case it is proposed to use Gaussian copula for the determination of joint distribution of shocks. Based on the simulated data analysis, statistical evidence was found in favor of the need to consider the leverage effect when modeling conditional volatility. Also, the results of the simulations demonstrated the advantage of the semi-nonparametric approach when the shape of the distribution deviates from normality. Finally, there were found evidence in favor of the proposed methods’ efficiency in application to the real data represented by the time series of Chevron Corporation and Exxon Mobil Corporation stock returns.