Modelling Overnight and Daytime Returns Using a Multivariate GARCH-Copula Model

We introduce a multivariate GARCH-Copula model to describe joint dynamics of overnight and daytime returns for multiple assets. The conditional mean and variance of individual overnight and daytime returns depend on their previous realizations through a variant of GARCH specification, and two Student’s t copulas describe joint distributions of both returns respectively. We employ both constant and time-varying correlation matrices for the t copulas and with the time-varying case the dependence structure of both returns depends on their previous dependence structures through a DCC specification. We estimate the model by a two-step procedure, where marginal distributions are estimated in the first step and copulas in the second. We apply our model to overnight and daytime returns of SPDR ETFs of nine major sectors and briefly illustrate its use in risk management and asset allocation. Our empirical results show higher mean, lower variance, fatter tails and lower correlations for overnight returns than daytime returns. Daytime returns are significantly negatively correlated with previous overnight returns. Moreover, daytime returns depend on previous overnight returns in both conditional variance and correlation matrix (through a DCC specification). Most of our empirical findings are consistent with the asymmetric information argument in the market microstructure literature. With respect to econometric modelling, our results show a DCC specification for correlation matrices of t copulas significantly improves the fit of data and enables the model to account for time-varying dependence structure.