• Medientyp: Sonstige Veröffentlichung; Bericht; E-Book
  • Titel: Log-modulated rough stochastic volatility models
  • Beteiligte: Bayer, Christian [Verfasser:in]; Harang, Fabian [Verfasser:in]; Pigato, Paolo [Verfasser:in]
  • Erschienen: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020
  • Ausgabe: published Version
  • Sprache: Englisch
  • DOI: https://doi.org/10.34657/8440; https://doi.org/10.20347/WIAS.PREPRINT.2752
  • ISSN: 2198-5855
  • Schlagwörter: fractional Brownian motion ; log Brownian motion ; Rough volatility models ; rough Bergomi model ; implied skew ; stochastic volatility
  • Entstehung:
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  • Beschreibung: 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.
  • Zugangsstatus: Freier Zugang