Log-modulated rough stochastic volatility models

@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
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References

SHOWING 1-10 OF 32 REFERENCES
Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint
  • 17
  • PDF
Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness
  • 5
  • PDF
Volatility Is Rough
  • 302
  • PDF
The Characteristic Function of Rough Heston Models
  • 130
  • PDF
Pricing Under Rough Volatility
  • 169
  • PDF
Short-time at-the-money skew and rough fractional volatility
  • 69
  • PDF
Is Volatility Rough
  • 20
  • PDF
A regularity structure for rough volatility
  • 35
  • PDF
Short-time near-the-money skew in rough fractional volatility models
  • 44
  • PDF
No-Arbitrage Implies Power-Law Market Impact and Rough Volatility
  • 24
  • PDF
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