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A regularity structure for rough volatility

Bayer, Christian; Friz, Peter; Gassiat, Paul; Martin, Jorg; Stemper, Benjamin (2020), A regularity structure for rough volatility, Mathematical Finance, 30, 3, p. 782-832. 10.1111/mafi.12233

Type
Article accepté pour publication ou publié
External document link
https://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/mafi.12233
Date
2020
Journal name
Mathematical Finance
Volume
30
Number
3
Publisher
Wiley
Pages
782-832
Publication identifier
10.1111/mafi.12233
Metadata
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Author(s)
Bayer, Christian
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Friz, Peter
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Martin, Jorg
Stemper, Benjamin
Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin] [WIAS]
Abstract (EN)
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.

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