Bayesian Monte Carlo Filtering for Stochastic Volatility Models

Modelling of the fi nancial variable evolution represents an important issue in financial econometrics. Stochastic dynamic models allow to describe more accurately many features of the financial variables, but often there exists a trade-off between the modelling accuracy and the complexity. Moreover the degree of complexity is increased by the use of latent factors which are usually introduced in time series analysis, in order to capture the heterogeneous time evolution of the observed process. The presence of unobserved components makes the maximum likelihood inference more difficult to apply. Thus the Bayesian approach is preferable since it allows to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The main aim of this work is to produce an updated review of Bayesian inference approaches for latent factor models. Moreover, we provide a review of simulation based filtering methods in a Bayesian perspective focusing, through some examples, on stochastic volatility models.