Comparison of Multivariate GARCH Models with Application to Zero-Coupon Bond Volatility

Abstract: The purpose of this thesis is to investigate different formulations of multivariate GARCH models and to apply two of the popular ones – the BEKK- GARCH model and the DCC- GARCH model – in evaluating the volatility of a portfolio of zero-coupon bonds. Multivariate GARCH models are considered as one of the most useful tools for analyzing and forecasting the volatility of time series when volatility fluctuates over time. This feature demonstrates its availability in modeling the co-movement of multivariate time series with varying conditional covariance matrix. From this point of view, firstly we focus on understanding the model specifications of several widely used multivariate GARCH models so as to select appropriate models; and then construct the BEKK form and the DCC form separately by employing the financial data obtained from the website of the European Central Bank. The next work is dedicated to diagnose the goodness of fit of the established models even though there are comparatively few tests specific to multivariate models according to previous literatures. On top of those, we compare the fitting performance of these two forms and predict the future dynamics of our data on the ground of these two models.