It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

•We study the dynamics of the log-realized volatility with a time-varying HAR.•Parameters are estimated with an on-line method.•The parameters of a two-factor stochastic volatility model are recursively estimated.•The vol-of-vol parameter of the slow factor increases during the financial crisis.•The increase of vol-of-vol generates higher persistence and higher variability.

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as an auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters.