Log-modulated rough stochastic volatility models

  title={Log-modulated rough stochastic volatility models},
  author={C. Bayer and F. Harang and Paolo Pigato},
  journal={arXiv: Mathematical Finance},
  • C. Bayer, F. Harang, Paolo Pigato
  • Published 2020
  • Mathematics, Economics
  • arXiv: Mathematical Finance
  • 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… CONTINUE READING
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