This thesis attempts to model and forecast returns and realized volatility using two different methods: time series models that exploit the historical information set and options-based approach that provides a natural forecast of return variation from listed option prices. Both univariate and multivariate estimation of the time series models are considered in our analysis.
Chapter 1: This chapter introduces a modified fractionally co-integrated vector autoregressive model, M-FCVAR, that caters for systems with I(0) and I(d) variables under the presence of long memory in the co-integrating residuals. Model inference of the FCVAR and M-FCVAR are compared using Monte Carlo simulations and an empirical application. The M-FCVAR is found to yield better in-sample fit and more precise model estimates. Higher return predictability is observed over long horizons using the M-FCVAR in the empirical example. In addition, the shocks associated with the I(0) variables could be permanent or transitory. We show that particular equation specifications are required to restrict these shocks when they produce only transitory effects on the I(d) variables. The simulation results show that the inappropriate treatment of the shock to the I(0) variable may negatively affect the precision in the estimation of the model parameters as well as the in-sample fit.
Chapter 2: This chapter evaluates the performance of various measures of model-free option-implied volatility in predicting returns and realized volatility. The critical role of the out-of-the money call options is highlighted through an investigation of the relevance of different components of the model-free implied volatility. The Monte Carlo simulations show that: first, volatility forecasting performance of measures of implied volatility can be enhanced by employing an interpolation-extrapolation technique; second, for most measures considered, gains in their predictive power for future returns can be obtained by implementing an interpolation procedure. An empirical application using SPX options recorded from 2003 to 2013 further illustrates these claims.
Chapter 3: This chapter compares the performance of various least absolute shrinkage and selection operator (Lasso) based models in forecasting future log realized variance (RV) constructed from high-frequency returns. We conduct a comprehensive empirical study using the SPY and 10 individual stocks selected from 10 different sectors. In an in-sample analysis, we provide evidence for the invalidity of the lag structure implied by the heterogeneous autoregressive (HAR) model which has been heavily adopted in volatility forecast. In our out-of-sample study considering the full time period, the best forecasting performance is usually provided by the Lasso-based model and the idea of forecast combination tends to improve the forecasting accuracy of the Lasso-based model. Among all models of interest, the ordered Lasso AR using the forecast combination serves as the top performer most frequently in forecasting RV and its improvements over the HAR model are, in most cases, significant over monthly horizons. Moreover, we observe a strong impact of the financial crisis on the performance of the Lasso-based models. Nevertheless, the ordered Lasso AR with the forecast combination still retains its advantages in the post-crisis period, especially over long horizons. In line with the existing study, the superiority of the Lasso-based models is more evident in a larger forecasting window size. The conclusions outlined above are not affected by the variation in the sampling frequency upon which the RV series are based. However, as the sampling frequency increases, there tends to be more situations where the Lasso-based model achieves the top performance in the full sample analysis.