A regularity structure for rough volatility
Bayer, Christian; Friz, Peter K.; Gassiat, Paul; Martin, Joerg; Stemper, Benjamin (2018), A regularity structure for rough volatility. https://basepub.dauphine.fr/handle/123456789/18481
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01936400
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
Friz, Peter K.
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Humboldt-Universität zu Berlin
Abstract (EN)A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extreme skews that were thought to be outside the scope of stochastic volatility. On the mathematical side, Markovianity and, partially, semi-martingality 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 provides a new and powerful tool to analyze rough volatility models.
Subjects / Keywordsstochastic; differential equations
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