Deep Learning Volatility

32 Pages Posted: 7 Feb 2019 Last revised: 20 Jul 2021

See all articles by Blanka Horvath

Blanka Horvath

ETH Zürich - Department of Mathematics

Aitor Muguruza

Imperial College London; Kaiju Capital Management

Mehdi Tomas

Ecole Polytechnique

Date Written: January 24, 2019


We present a neural network based calibration method that performs the calibration task within
a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models—including second generation stochastic volatility
models and the rough volatility family—and a range of derivative contracts. Neural networks in
this work are used in an off-line approximation of complex pricing functions, which are difficult
to represent or time-consuming to evaluate by other means. The form in which information
from available data is extracted and used influences network performance: The grid-based algorithm used for calibration, inspired by representing the implied volatility and option prices as a
collection of pixels is extended to include models where the initial forward variance curve is an
input. We highlight how this perspective opens new horizons for quantitative modelling. The
calibration bottleneck posed by a slow pricing of derivative contracts is lifted, and stochastic
volatility models (classical and rough) can be handled in great generality. We demonstrate the
calibration performance both on simulated and historical data, on different derivative contracts
and on a number of examples models of increasing complexity, and also showcase some of the
potentials of this approach towards model recognition. The algorithm and examples are provided in the Github repository GitHub: NN-StochVol-Calibrations.

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 Zürich - Department of Mathematics ( email )

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

Aitor Muguruza (Contact Author)

Imperial College London ( email )

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

Kaiju Capital Management ( email )

Mehdi Tomas

Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128

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