Introduction
Volatility, defined as the periodic (annualized) standard deviation of financial asset returns, is a critical factor in financial markets. Consequently, modeling volatility has become a matter of paramount importance. Historically, volatility modelling presents two persistent stylised facts. The first one is the presence of long memory features in volatility. Long memory is exhibited in a stationary process if its covariance function decays slowly. The second stylised fact is the leverage effect which is the existence of the negative correlation between price increments and volatility increments. Recent empirical evidence suggests that most financial markets exhibit the so-called rough volatility dynamics or irregular behaviour over time which is modelled via a fractional Brownian motion (fBm) (see Mandelbrot and Ness (1968)) with a Hurst parameter between 0 and 0.5. This empirical observation is credited to the availability of high-frequency datasets and modelling volatility dynamics using rough specifications offers improved pricing, hedging and forecasting performance (see for example Bayer et al (2016), Gatheral et al (2018), Alfeus and Nikitopoulos (2022)).
