It’s all about volatility of volatility: evidence from a two-factor stochastic volatility model

The persistent nature of equity volatility is investigated by means of a multi-factorstochastic volatility model with time varying parameters. The parameters are estimated bymeans of a sequential matching procedure which adopts as 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. As a consequence of the dynamics in the stochastic volatility parameters, the shape and curvature of the volatility smile evolve trough time.