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Article Dans Une Revue Mathematical Finance Année : 2020

A regularity structure for rough volatility

Résumé

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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Dates et versions

hal-03003124 , version 1 (27-11-2018)
hal-03003124 , version 2 (03-05-2023)

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Christian Bayer, Peter Friz, Paul Gassiat, Jorg Martin, Benjamin Stemper. A regularity structure for rough volatility. Mathematical Finance, 2020, 30 (3), pp.782-832. ⟨10.1111/mafi.12233⟩. ⟨hal-03003124v2⟩
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