This thesis studies three important topics in modeling financial volatility. First, the jump clustering in ex post variance and its implications on forecasting, second, the underlying distribution of stochastic volatility and third, the role of non-Gaussian multivariate return distribution combined with a realized GARCH framework. The first chapter is on variance jumps. Financial markets present unexpected and large jumps, due to unobserved news flow. I focus on modeling the ex post variance jumps, their time- dependent arrivals and their sizes. I use a discrete-time bivariate model, with two autoregressive components which capture the long and short-run memory of the ex post variance measures. I estimate contemporaneous and time-dependent jumps in the log-measures of realized variance and bipower variation. The results from S&P500 show that the variance jumps are frequent and persistent. I examine the ability of jumps to forecast returns and ex post variance densities over horizons of up to 50 days out-of-sample. Modeling jumps significantly improves ex post variance density forecasts for all horizons and improves forecasts of the returns density. In the second chapter I explore the empirical non-Gaussian features of stochastic volatility. The standard assumption in a stochastic volatility specification is typically a restrictive Gaussian AR(1) structure. I drop this assumption and instead I assume that latent log-volatility follows an infinite mixture of normals with a Dirichlet process prior. The ex post measure of realized variance is used as a source of information to help identify the unknown distribution of log- volatility. Results from major stock indices show strong evidence of non-Gaussian distributional behaviour of volatility. The proposed framework captures asymmetry and thick tails in returns as well as realized variance. In out-of-sample forecasting, the new model provides improved density forecasts for returns, negative returns and log-realized variance. In the third chapter a new approach for multivariate realized GARCH models is proposed. Two new extensions that have non-Gaussian innovations are developed. The first one is a parametric version, with multivariate-t innovations. The second one is a nonparametric approximation of the return distribution using an infinite mixture of multivariate normals given a Dirichlet process prior. The proposed models are based on the assumption that the realized covariance follows an Inverse Wishart distribution with conditional mean set to the conditional covariance of returns. The benefits of the proposed models are demonstrated from density forecasting and portfolio applications. Results from two equity datasets indicate that modeling the tail behaviour improves return density forecasting compared to the Gaussian assumption. The proposed models produce the least volatile global minimum variance portfolios out-of-sample and provide improved forecasts of Value-at-Risk and Expected Shortfall. / Thesis / Doctor of Business Administration (DBA)