@article{Bayer2020LogmodulatedRS,
title={Log-modulated rough stochastic volatility models},
author={Christian Bayer and F. Harang and Paolo Pigato},
journal={arXiv: Mathematical Finance},
year={2020}
}

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… Expand