Abstract
This chapter describes the concepts and methods related to the modeling of stochastic volatility (SV), that is, the occurrence of time heterogeneity in the variances and covariances of asset returns. Section 7.2 explains how to deal with the latent nature of SV using, in particular, the Kalman filter to propose methods of inference. Section 7.3 illustrates how these techniques can be applied to estimate simple SV models using maximum likelihood methods and presents alternative approaches that overcome the major limitations of the linear Kalman filter. Section 7.4 presents a few leading extensions of the SV model described in the recent literature. Finally, Section 7.5 performs a comparison between GARCH-type models described in Chapters 5 and 6, and SV models.
Keywords: Stochastic volatility; Kalman filter; multifactor volatility model; filtering; normal mixture model; GARCH-diffusion model
Essentials of Time Series for Financial Applications 