Book Description

Volatility modeling and forecasting are crucial in risk management and pricing derivatives. High-frequency financial data are dynamic and affected by the microstructure noise. For the univariate case, we define the two-scale realized volatility estimator as the measure of the volatility of high-frequency financial data. Two main models for volatility, Generalized Autoregressive Conditional Heteroscedastic (GARCH) and Heterogeneous Autoregressive (HAR), are evaluated and compared for the realized volatility forecast of four major stock indices high-frequency data. We also consider the measures of jump component and heteroskedasticity of the error in the extended HAR models. For the improvement of forecasting accuracy of realized volatility, this dissertation develops hybrid forecasting models combining the GARCH and HAR family models with the machine learning methods, Support Vector Regression(SVR), Extreme Gradient Boosting (XGBoost), Long Short-Term Memory (LSTM) and Transformer. We construct hybrid models using the outputs of the GARCH and HAR family models. In the empirical application, we demonstrate improvements of the hybrid models for one-day ahead realized volatility forecast accuracy. The results show that the hybrid LSTM and Transformer based models provide more accurate forecasts than the other models. In the financial markets, it is well accepted that the volatilities are time-varying correlated across the indices. We construct two portfolios, the Index portfolio and the Forex portfolio. The Index portfolio contains three major stock indices, and the Forex portfolio includes three major exchange rates. We model the conditional covariances of the two portfolios with BEKK, DCC-GARCH, and Vector HAR. The hybrid models combine the estimations of traditional multivariate models and the machine learning framework. Results of the study indicate that for one-day ahead volatility matrix forecasting, these hybrid models can achieve better performance than the traditional models for the two portfolios.