Deep Learning Volatility

41 Pages Posted: 7 Feb 2019 Last revised: 28 Feb 2019

See all articles by Blanka Horvath

Blanka Horvath

ETH Zurich - Department of Mathematics

Aitor Muguruza

Imperial College London

Mehdi Tomas

Ecole Polytechnique

Date Written: January 24, 2019


We present a consistent neural network based calibration method for a number of volatility models-including the rough volatility family-that performs the calibration task within a few milliseconds for the full implied volatility surface.

The aim of neural networks in this work is an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. We highlight how this perspective opens new horizons for quantitative modelling: The calibration bottleneck posed by a slow pricing of derivative contracts is lifted. This brings several model families (such as rough volatility models) within the scope of applicability in industry practice. As customary for machine learning, the form in which information from available data is extracted and stored is crucial for network performance. With this in mind we discuss how our approach addresses the usual challenges of machine learning solutions in a financial context (availability of training data, interpretability of results for regulators, control over generalisation errors). We present specific architectures for price approximation and calibration and optimize these with respect different objectives regarding accuracy, speed and robustness. We also find that including the intermediate step of learning pricing functions of (classical or rough) models before calibration significantly improves network performance compared to direct calibration to data.

Keywords: Rough volatility, volatility modelling, Volterra process, machine learning, accurate price approximation, calibration, model assessment, Monte Carlo

JEL Classification: 60G15, 60G22, 91G20, 91G60, 91B25

Suggested Citation

Horvath, Blanka and Muguruza, Aitor and Tomas, Mehdi, Deep Learning Volatility (January 24, 2019). Available at SSRN: or

Blanka Horvath

ETH Zurich - Department of Mathematics ( email )

R¨amistrasse 101
Z¨urich, 8092

Aitor Muguruza (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Mehdi Tomas

Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128

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