From rough to multifractal volatility: The log S-fBM model

Peng Wu, Jean-François Muzy and Emmanuel Bacry

Physica A: Statistical Mechanics and its Applications, 2022, vol. 604, issue C

Abstract: We introduce a family of random measures MH,T(dt), namely log S-fBM, such that, for H>0, MH,T(dt)=eωH,T(t)dt where ωH,T(t) is a Gaussian process that can be considered as a stationary version of an H-fractional Brownian motion. Moreover, when H→0, one has MH,T(dt)→M˜T(dt) (in the weak sense) where M˜T(dt) is the celebrated log-normal multifractal random measure (MRM). Thus, this model allows us to consider, within the same framework, the two popular classes of multifractal (H=0) and rough volatility (0Keywords: Rough volatility; Multifractal volatility; Fractional Brownian motion; GMM estimation; Intermittency coefficient (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:604:y:2022:i:c:s0378437122005866

DOI: 10.1016/j.physa.2022.127919

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