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A regularity structure for rough volatility
Author(s) -
Bayer Christian,
Friz Peter K.,
Gassiat Paul,
Martin Jorg,
Stemper Benjamin
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12233
Subject(s) - stylized fact , stochastic volatility , volatility (finance) , implied volatility , econometrics , volatility smile , economics , forward volatility , volatility swap , sabr volatility model , mathematics , keynesian economics
Abstract 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.