Factor Stochastic Volatility (FSV) models are useful for managing investment risk and constructing portfolios. They possess a latent low-dimensional random process to help explain a higher-dimensional vector of finacial returns. This hidden process can represent anything the investor deems pertinent Despite being expressive models in this class are exceedingly difficult to estimate. Within a Bayesian framework Gibbs sampling is the most common approach yet this is only available for some models used along with certain priors. Variants of Metropolis-Hastings are theoretically justified however they do not mix well in practice. We argue that Particle Markov chain Monte Carlo techniques a newer set of likehood-free MCMC algorithms are well-suited to this task. We describe the general principles of the algorithm strategies for parallelization and show some examples of estimating different models. We also demonstrate once these models are estimated their out-of-sample forecasting performance.
