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Pathwise large deviations for the rough Bergomi model

Part of: Mathematical finance Stochastic processes Limit theorems

Published online by Cambridge University Press:  16 January 2019

Antoine Jacquier ,
Mikko S. Pakkanen  and
Henry Stone
Antoine Jacquier*
Affiliation:
Imperial College London
Mikko S. Pakkanen*
Affiliation:
Imperial College London CREATES
Henry Stone*
Affiliation:
Imperial College London
*
* Postal address: Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
* Postal address: Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
* Postal address: Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
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Abstract

Introduced recently in mathematical finance by Bayer et al. (2016), the rough Bergomi model has proved particularly efficient to calibrate option markets. We investigate some of its probabilistic properties, in particular proving a pathwise large deviations principle for a small-noise version of the model. The exponential function (continuous but superlinear) as well as the drift appearing in the volatility process fall beyond the scope of existing results, and a dedicated analysis is needed.

Keywords

Rough volatilitylarge deviationssmall-time asymptoticsGaussian measurereproducing kernel Hilbert space

MSC classification

Primary: 60F10: Large deviations
Secondary: 60G22: Fractional processes, including fractional Brownian motion 91G20: Derivative securities 60G15: Gaussian processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1078 - 1092
Copyright
Copyright © Applied Probability Trust 2018 

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