Modeling overnight and daytime returns using a multivariate generalized autoregressive conditional heteroskedasticity copula model

Long Kang and Simon H. Babbs

Journal of Risk

Abstract: ABSTRACT We introduce a multivariate generalized autoregressive conditional heteroskedasticity (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 t copulas describe joint distributions of overnight and daytime returns, respectively. We employ both constant and time-varying correlation matrices for the t copulas. In the time-varying case, the dependence structure of both returns depends on their previous dependence structures through a dynamic conditional correlation (DCC) specification. We estimate the model using a two-step procedure, where marginal distributions are estimated in the first step and copulas are estimated in the second. We apply our model to overnight and daytime returns of fifteen funds of different types, and illustrate its applications in risk management and asset allocation. Our empirical results show (for most tested assets) higher means, lower variance and fatter tails for overnight returns than daytime returns. The comparison results of dependence between overnight and daytime returns are mixed. 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 modeling, our results show that 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.

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