Essays on multivariate stochastic volatility models - CHEN, Han (Institutional Knowledge at Singapore Management University, 2020)
In this dissertation, I have made several contributions to the literature on the multivariate stochastic volatility model. First, I have considered a new multivariate stochastic volatility (MSV) model based on a recently proposed novel parameterization of the correlation matrix. This modeling design is a generalization of Fisher's z-transformation to the high-dimensional case. It is fully flexible as the validity of the resulting correlation matrix is guaranteed automatically. It allows me to completely separate the driving factors of volatilities and correlations. To conduct an econometric analysis of the proposed model, I develop a new Bayesian method that relies on the Markov Chain Monte Carlo (MCMC) tool. For the latent variables, the traditional single-move or multi-move sampler is replaced by a novel technique called Particle Gibbs Ancestor Sampling (PGAS), which is built upon the Sequential Monte Carlo (SMC) method. Simulation results indicate that our algorithm performs well when a small number of particles are used. Empirical studies based on the exchange rate returns and equity returns are considered and reveal some interesting empirical results. Second, I further develop a multivariate stochastic volatility model with intra-day realized measures. A simple and consistent estimation technique is developed. The problem of under-identification is discussed. A two-stage approach is introduced to address the problem. A simulation study shows that the proposed method works well in finite samples. The new model is then implemented using two financial datasets. A comparison with some existing models is made. Third, I also incorporate the leverage effect and the heavy-tailed error distribution into the MSV model. 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 stock indices are considered. I have found strong evidence of the leverage effect and, more, importantly, heavy-tails in the errors.