A regularity structure for rough volatility

By Christian Bayer, Peter K. Friz, Paul Gassiat, Jorg Martin, Benjamin Stemper. Mathematical Finance, 2017

75 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/b096549f4a8738009b97d53836b595a04a3e797a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Short-time near-the-money skew in rough fractional volatility models (2017, methodology): “It was pointed out in Bayer et al. (2017) that a similar reasoning is possible when H < 1/2, the rough path is then replaced by a ‘richer enhancement’ of (B, Z), the precise size of which depends on H, for which again one has a LDP.”