WIAS Preprint No. 2752, (2020)

Log-modulated rough stochastic volatility models


  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Harang, Fabian
  • Pigato, Paolo

2010 Mathematics Subject Classification

  • 91G30 60G22


  • Rough volatility models, stochastic volatility, rough Bergomi model, implied skew, fractional Brownian motion, log Brownian motion




We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the limit case of vanishing Hurst index H. The so-obtained log-modulated fractional Brownian motion (log-fBm) is a continuous Gaussian process even for H = 0. As a consequence, the resulting super-rough stochastic volatility models can be analysed over the whole range of Hurst indices between 0 and 1/2, including H = 0, without the need of further normalization. We obtain the usual power law explosion of the skew as maturity T goes to 0, modulated by a logarithmic term, so no flattening of the skew occurs as H goes to 0.

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