Modeling multiple asset returns by a time-varying t copula model

Abstract

We illustrate a framework to model joint distributions of multiple asset returns using a time-varying Student′s t copula model. We model marginal distributions of individual asset returns by a variant of GARCH models and then use a Student′s t copula to connect all the margins. To build a time-varying structure for the correlation matrix of t copula, we employ a dynamic conditional correlation (DCC) specification. We illustrate the two-stage estimation procedures for the model and apply the model to 45 major US stocks returns selected from nine sectors. As it is quite challenging to find a copula function with very flexible parameter structure to account for difference dependence features among all pairs of random variables, our time-varying t copula model tends to be a good working tool to model multiple asset returns for risk management and asset allocation purposes. Our model can capture time-varying conditional correlation and some degree of tail dependence, while it also has limitations of featuring symmetric dependence and inability of generating high tail dependence when being used to model a large number of asset returns.​