Abstract
This thesis consists of four essays in financial econometrics. Chapter 2 focuses on modelling and forecasting the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) using a time-varying parameter heterogeneous autoregressive (TVP-HAR) model. Chapter 3 investigates the heterogeneous volatility information content in the Realized Generalized Autoregressive Conditional Heteroskedasticity (Realized GARCH) framework for modelling and forecasting volatility. Chapter 4 examines discrete-time stochastic volatility (SV) models, the CBOE one-day Volatility Index (VIX1D), and the one-day volatility risk premium (VRP). The final chapter, Chapter 5, explores the economic value of forecasts and strategy gains in volatility timing. Overall, this thesis contributes to the growing literature on modelling and forecasting two key measures of volatility, namely the option-implied VIX and realized volatility (RV), and underscores their practical relevance for portfolio management and option pricing.
In Chapter 2, we propose a time-varying parameter heterogeneous autoregressive (TVP-HAR) model to model and forecast the CBOE VIX. To demonstrate its superiority, we consider six variations of the model with different bandwidths and smoothing variables, and include the constant-coefficient HAR model as a benchmark. We show that the TVP-HAR models outperform the constant-coefficient HAR model in both modelling and forecasting the VIX. Among the TVP-HAR specifications, the VIX futures-driven coefficient model with a rule-of-thumb bandwidth delivers the best performance for investors in forecasting market risk and informing hedging strategies.
Chapter 3 investigates the role of heterogeneous volatility measures, including the CBOE VIX, the one-day volatility index (VIX1D), realized volatility (RV), and the daily range, in conditional volatility estimation and forecasting within the Realized GARCH framework. To evaluate their impact, we first construct a volatility response function, defined as the difference between one-step-ahead conditional volatility forecasts incorporating both return and volatility information and those based solely on return innovations. We then compute the variance share to assess the contribution of each measure in explaining future variation in conditional volatility. Our results show that, among the four measures, the VIX is the most informative for the Realized GARCH model in both modelling and forecasting volatility.
In Chapter 4, we focus on stochastic volatility (SV) models and contrast them with GARCH models in the context of option pricing. Our motivation stems from the recent introduction of the CBOE VIX1D and the persistently positive short-term volatility risk premium (VRP). This empirical evidence highlights the importance of pricing short-term volatility risk and challenges GARCH models, which imply a zero one-day VRP under the local risk-neutral valuation relationship (LRNVR). To address this inconsistency, we propose a hybrid VIX1D-implied stochastic volatility-in-mean (VSVM) model. We show that the LRNVR assumption does not hold within a stochastic volatility framework, allowing the VSVM model to better capture the dynamics of the one-day VRP. We further demonstrate that forecasting VIX and RV are two fundamental tasks, and that SV models are better suited than GARCH models to address them jointly.
The final chapter (Chapter 5) broadens the scope from univariate volatility forecasting to covariance forecasting based on multiple return series. Building on the literature that identifies two sources of economic gains from volatility timing: covariance forecasting and portfolio construction. This chapter integrates both perspectives by evaluating three covariance models, namely the Dynamic Conditional Correlation GARCH (DCC), the range-based Multiplicative Error Model (MEM), and the Multivariate Stochastic Volatility (MSV) model, together with three portfolio strategies: minimum variance (MIN), maximum return (MAX), and volatility-managed (VM). Our results indicate that the MSV framework consistently outperforms DCC and MEM, highlighting the importance of stochastic volatility in improving covariance estimation. On the strategy side, both MAX and VM deliver higher economic value than MIN. However, there is no consistent evidence that VM dominates MAX, suggesting that volatility-managed strategies do not always outperform the general mean–variance framework.