Essays on Multivariate Stochastic Volatility Models

In this dissertation, we make a few contributions to the literature of the multivariate stochastic volatility model. We first consider a new multivariate stochastic volatility (MSV) model, applying a recently proposed novel parameterization of the correlation matrix. This modeling design is a generalization of Fisher's Z-transformation to high-dimensional case and it is fully flexible as the validity of the resulting correlation matrix is guaranteed automatically, which allows us to completely separate the driving factors of volatilities and correlations. A different estimation tool is proposed. Similar to much of the existing literature on MSV, we work within a Bayesian framework and hence rely on Markov Chain Monte Carlo (MCMC) tool. When dealing with latent variables, traditional single-move or multi-move sampler is replaced by a novel technique called Particle Gibbs Ancestor Sampling (PGAS), which is built upon Sequential Monte Carlo (SMC) method. We further develop a multivariate stochastic volatility model with intra-day realized measures. Firstly, we purpose a simple and consistent estimation for the realized multivariate stochastic volatility model. Secondly, we discuss the under-identified issues in finite samples and propose to use a two-stage approach to reduce the estimation bias of some parameters. As important extensions, we also incorporate the cross leverage effect and the fat tail unconditional error distribution into the MSV model with dynamic correlation. A Particle Gibbs Sampling Algorithm is developed for the extended MSV model. Simulation results indicate that our algorithm performs well when a small number of particles are used. Empirical studies of the exchange rate returns and equity returns are considered and reveal interesting empirical results.