A regularity structure for rough volatility

Christian Bayer (1) , Peter K. K Friz (1, 2) , Paul Gassiat (3) , Joerg Martin (4) , Benjamin Stemper (1, 2)

1 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
2 TU - Technical University of Berlin / Technische Universität Berlin
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin

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.

Domaines: Probabilités [math.PR]

Christian Bayer, Peter K. K Friz, Paul Gassiat, Joerg Martin, Benjamin Stemper. A regularity structure for rough volatility. 2018. ⟨hal-03003124v1⟩