Modelling and Forecasting of Stochastic Volatility and Jumps

The thesis reviews the most commonly used volatility forecasting models from the ARCH/GARCH, realized volatility and stochastic volatility forecasting frameworks, with the main focus being placed on Stochastic-Volatility Jump-Diffusion (SVJD) models, on the ways of how high-frequency power-variation estimators can be used in SVJD model setting, and on the use of Bayesian methods for the estimation of SVJD model parameters and latent states. SVJD-RV-Z class of models is developed, utilizing the realized variance for better estimation of the stochastic variances, and the non-parametric Z-Estimator for more accurate estimation of price jumps. Several adapted particle filters, specifically designed for latent-state filtering in SVJD models, are derived, and a Sequential Gibbs Particle Filter (SGPF) algorithm is developed for the sequential learning of their parameters. In the empirical study, four SVJD models (with intraday data, self-exciting jumps in prices and volatility, as well as multiple volatility components) are applied for the task of realized volatility forecasting on the time series of 7 foreign exchange rates and 10 ETF/ETN securities in the daily, weekly and monthly forecast horizon. The performance of the SVJD models is compared with 3 GARCH models (GARCH, EGARCH and GJRGARCH), 15 HAR model specifications (HAR, AHAR, SHAR, HARJ and HARQ), and 15 Echo State Neural Network (ESN) based volatility models developed by the author. The SVJD-RV-Z models with jumps in volatility and prices are shown to exhibit the highest out-sample predictive power, comparable to the best HAR and ESN model specifications.