Asymptotic Behaviour of Randomised Fractional Volatility Models

23 Pages Posted: 7 Aug 2017 Last revised: 15 Jun 2018

See all articles by Blanka Horvath

Blanka Horvath

ETH Zürich - Department of Mathematics

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Chloe Lacombe

Imperial College London

Date Written: August 3, 2017

Abstract

We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail behaviours in particular). In order to do so, we extend some results on sample path large deviations for such diffusions. As an application, we show how these results characterise the small-time and tail estimates of the implied volatility for rough volatility models, recently proposed in mathematical finance.

Keywords: Rough volatility, large deviations, implied volatility asymptotics

Suggested Citation

Horvath, Blanka and Jacquier, Antoine and Lacombe, Chloe, Asymptotic Behaviour of Randomised Fractional Volatility Models (August 3, 2017). Available at SSRN: https://ssrn.com/abstract=3013658 or http://dx.doi.org/10.2139/ssrn.3013658

Blanka Horvath

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Chloe Lacombe

Imperial College London ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

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