Linear state models for volatility estimation and prediction

Abstract

This thesis concerns the calibration and estimation of linear state models for forecasting stock return volatility. In the first two chapters I present aspects of financial modelling theory and practice that are of particular relevance to the theme of this present work. In addition to this I review the literature concerning these aspects with a particular emphasis on the area of dynamic volatility models. These chapters set the scene and lay the foundations for subsequent empirical work and are a contribution in themselves. The structure of the models employed in the application chapters 4,5 and 6 is the state-space structure, or alternatively the models are known as unobserved components models. In the literature these models have been applied in the estimation of volatility, both for high frequency and low frequency data. As opposed to what has been carried out in the literature I propose the use of these models with Gaussian components. I suggest the implementation of these for high frequency data for short and medium term forecasting. I then demonstrate the calibration of these models and compare medium term forecasting performance for different forecasting methods and model variations as well as that of GARCH and constant volatility models. I then introduce implied volatility measurements leading to two-state models and verify whether this derivative-based information improves forecasting performance. In chapter 6I compare different unobserved components models' specification and forecasting performance. The appendices contain the extensive workings of the parameter estimates' standard error calculations.