Statistical analysis of some financial time series models

The aim of this dissertation is to study the dynamics of asset returns under both the physical measure and the risk neutral measure. It consists of two different research topics.;The first topic is primarily concerned with a specific class of volatility component models. This family of models have received much attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or non-stationarity in asset price volatility. The first part of the dissertation focuses on their probabilistic properties and statistical inference on these models is discussed as well.;The second topic pertains to the distributional approximations of risk neutral distribution of asset returns for the purpose of option pricing. Risk neutral measures are a key ingredient of financial derivative pricing. Much effort has been devoted to characterizing the risk neutral distribution pertaining to the underlying asset. The rest of the dissertation studies the Generalized Hyperbolic family of distributions and examines their applications in option pricing.