The thesis studies three different conditional correlation Multivariate GARCH (MGARCH) models. They are the Constant Conditional Correlation (CCC-) GARCH, Dynamic Conditional Correlation (DCC-) GARCH and Asymmetric Dynamic Conditional Correlation (ADCC-) GARCH, in which the time-varying volatilities are modelled by three univariate GARCH models with the error term assumed to have a Gaussian distribution. In order to compare the performance of these models, we apply them to the volatility analysis of two stocks. Regarding model inference, we adopt a Bayesian approach and implement a Markov Chain Monte Carlo (MCMC) algorithm, Metropolis Within Gibbs (MWG), instead of the regular maximum likelihood (ML) method. Finally, the estimated models are employed to compute Value at Risk (VaR) and their performance is discussed.
