Volatility Model Calibration With Convolutional Neural Networks

12 Pages Posted: 14 Oct 2018

See all articles by Georgi Dimitroff

Georgi Dimitroff

Independent

Dirk Röder

DZ Bank AG

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Date Written: September 20, 2018

Abstract

We use a supervised deep convolution neural network to replicate the calibration of the Heston model to equity volatility surfaces. For this purpose we treat the implied volatility surface together with some auxiliary data, namely the strikes and moneyness of the corresponding options and the equity forwards, as a 3-dimensional input tensor for the neural network, in analogy to a colour channel image representation like the RGB. To extract the main features of the input data we are using inception layers with (1;1), (1;3) and (2;1) dimensional kernels. The specific choice is motivated by the no-arbitrage conditions on the call price surface. In terms of a local surface modelling the (1;3) filters with different weights can model the position, slope and curvature in the moneyness direction while the (2;1) filters can model Position and slope in the maturity direction. The neural network has been implemented using the open source library tensorflow.

Keywords: Heston Model, Convolutional Neural Network, Deep Learning, Machine Learning, Volatility Model Calibration

JEL Classification: C45

Suggested Citation

Dimitroff, Georgi and Röder, Dirk and Fries, Christian P., Volatility Model Calibration With Convolutional Neural Networks (September 20, 2018). Available at SSRN: https://ssrn.com/abstract=3252432 or http://dx.doi.org/10.2139/ssrn.3252432

Dirk Röder

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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