Damian, C., & Frey, R. (2022, April 1). Filtering and Parameter Estimation in a Rough Volatility Model [Conference Presentation]. XXIII Workshop on Quantitative Finance (QFW2022), Rome, Italy. http://hdl.handle.net/20.500.12708/153938
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.