A regularity structure for rough volatility

Artikel

A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key-stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside the scope of stochastic volatility models. On the mathematical side, Markovianity and, partially, semimartingality are lost. In this paper, we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provide a new and powerful tool to analyze rough volatility models.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Mathematical Finance ; ISSN: 1467-9965 ; Volume: 30 ; Year: 2019 ; Issue: 3 ; Pages: 782-832 ; Hoboken, NJ: Wiley

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Bayer, Christian ; Friz, Peter K. ; Gassiat, Paul ; Martin, Jorg ; Stemper, Benjamin
• Event: Veröffentlichung
• (who): Wiley
• (where): Hoboken, NJ
• (when): 2019

Further information

• DOI: doi:10.1111/mafi.12233
• Handle: http://hdl.handle.net/10419/230116
• Last update: 10.03.2025, 11:43 AM CET