From Rough to Multifractal volatility: the log S-fBM model

Peng Wu, Jean-François Muzy, Emmanuel Bacry

We introduce a family of random measures $M_{H,T}(dt)$, namely log S-fBM, such that, for $H>0$, $M_{H,T}(dt)=e^{{\omega }_{H,T}(t)}dt$ where ${\omega }_{H,T}(t)$ is a Gaussian process that…