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Rough Volatility - from microstructural foundations to smile

Banff International Research Station for Mathematical Innovation and Discovery

It has been recently shown that rough volatility models reproduce very well the statistical properties of low frequency financial data. In such models, the volatility process is driven by a fractional Brownian motion with Hurst parameter of order 0.1. Furthermore, it is very well-known that volatility and price movements are correlated, through the so-called leverage effect phenomenon. The goal of this talk is first to explain how fractional dynamics and leverage effect can be obtained from the behaviour of market participants at the microstructural scales. Using Hawkes processes, we show that these features naturally arise in the presence of high frequency trading under no arbitrage condition. Then we will demonstrate that such result enables us to derive an efficient method to compute the smile in rough volatility models. (This is joint work with Omar El Euch, Masaaki Fukasawa, Jim Gatheral and Thibault Jaisson.)

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes

video/mp4

Author affiliation: Université Pierre et Marie Curie (Paris 6)

2017-01-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59781

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/