Essays on Econometric Models of Volatility

This thesis contributes to the literature on volatility forecasting, focusing on the VIX index, the VIX futures and the VVIX. It consists of three main chapters. The first contribution is the introduction of a new VIX forecasting methodology employing both filtered historical simulations and four well-established indices. We examine the forecasting performance of three different GARCH models from 2011-2017. Our empirical results show that this new method outperforms the benchmark model which only uses the VIX index and assumes a normal distribution. Also, our proposed methodology is found to reduce the computational time significantly, compared to the traditional model which uses cross-sectional options prices. The second contribution is studying the role of the VIX term structure in predicting VIX futures prices. The estimation is carried out under the GJR model, assuming the empirical innovation density under the risk-neutral measure. Several models are employed differing in the data set used, i.e., futures data, or the VIX term structure, or their combinations. We find that the use of the VIX term structure improves the VIX futures forecasts, especially for the long-term VIX futures or when the VIX level is high. Also, the evidence from the 2020 COVID-19 crisis shows that using both the VIX term structure and the VIX futures provides lower pricing errors compared to using futures data only. The third contribution is an investigation on the optimal forecasts of the VVIX. This thesis presents a comparison of VVIX forecasts based on three individual models, eight combining methods and two LASSO-type regressions. Our finding is that the simple median combining method gives the lowest forecasting errors across the years among all the methods considered. Moreover, the model selection results of LASSO suggest that instead of daily changes in the VVIX, the changes in monthly VVIX are essential to predict the VVIX