4 papers
The Log S-fBM model: Statistical analysis
Othmane Zarhali, Emmanuel Bacry, Jean-François Muzy
The Log S-fBM model, introduced by Wu et al., is a stochastic volatility model whose log volatility is a stationary fractional Brownian motion (S-fBM): a stationary Gaussian proces…
Fast simulation of Volterra processes using random Fourier features with application to the log-stationary fractional Brownian motion
Othmane Zarhali, Nicolas Langrené
A fast simulation framework for stochastic Volterra processes based on Random Fourier Features (RFF) approximation of the kernel is developed. After recalling the main properties o…
From rough to multifractal multidimensional volatility: A multidimensional Log S-fBM model
Othmane Zarhali, Emmanuel Bacry, Jean-François Muzy
We introduce the multivariate Log S-fBM model (mLog S-fBM), extending the univariate framework proposed by Wu \textit{et al.} to the multidimensional setting. We define the multidi…
A Nested Factor Model for Equity Markets: Reconciling Multifractal Stock Returns and Rough Index Volatilities
Othmane Zarhali, Cecilia Aubrun, Emmanuel Bacry +2
The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the…