  In this paper, we focus on the estimation of historical volatility of asset
prices from high-frequency data. Stochastic volatility models pose a major
statistical challenge: since in reality historical volatility is not
observable, its current level and, possibly, the parameters governing its
dynamics have to be estimated from the observable time series of asset prices.
To complicate matters further, recent research has analyzed the rough behavior
of volatility time series to challenge the common assumption that the
volatility process is a Brownian semimartingale. In order to tackle the arising
inferential task efficiently in this setting, we use the fact that a fractional
Brownian motion can be represented as a superposition of Markovian
semimartingales (Ornstein-Uhlenbeck processes) and we solve the filtering (and
parameter estimation) problem by resorting to more standard techniques, such as
particle methods.
