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Peter Carr and Andrey Itkin apply a Markovian approximation of the fractional Brownian motion, known as the Dobrić-Ojeda process, to the
fractional stochastic volatility model, where the instantaneous variance is modelled using a lognormal process with drift and fractional
diffusion

Gatheral et al (2014) discovered that historical volatility time series exhibit behaviour that is much rougher than that of a Brownian motion for a wide range of assets. These authors