Approximate Factor Models with a Common Multiplicative Factor for Stochastic Volatility

Common factor stochastic volatility (CSV) models capture the commonality that is often observed in volatility patterns. However, they assume that all the time variation in volatility is driven by a single multiplicative factor. This paper has two contributions. Firstly, we develop a novel CSV model in which the volatility follows an inverse gamma process (CSV-IG), which allows for more extreme values in the volatility. We obtain an analytic expression for the likelihood of this CSV model, which greatly facilitates the numerical calculation of the marginal and predictive likelihood for model comparison. We also show that it is possible to simulate exactly from the posterior distribution of the volatilities using mixtures of gammas. Secondly, we generalize this CSV-IG model by parsimoniously substituting conditionally homoscedastic shocks with heteroscedastic factors which interact with the common multiplicative factor in an approximate factor model (CSV-IG-AF). In empirical applications, we show that our models have the best empirical performance. We also show that, even when allowing for more general complex volatility processes, it is important to specify a common multiplicative factor, as this substantially improves the empirical fit of the model.