VolGAN: a generative model for arbitrage-free implied volatility surfaces

32 Pages Posted: 28 Nov 2023 Last revised: 21 Dec 2023

See all articles by Milena Vuletić

Milena Vuletić

University of Oxford

Rama Cont

University of Oxford

Date Written: October 30, 2023

Abstract

We introduce VolGAN, a generative model for arbitrage-free implied volatility surfaces. The model is trained on time series of implied volatility surfaces and underlying prices and is capable of generating realistic scenarios for joint dynamics of the implied volatility surface and the underlying asset. We illustrate the performance of the model by training it on SPX implied volatility time series and show that it is able to learn the covariance structure of the co-movements in implied volatilities and generate realistic dynamics for the (VIX) volatility index. In particular, the generative model is capable of simulating scenarios with non-Gaussian distributions of increments for state variables as well as time-varying correlations.

Keywords: GAN, generative models, implied volatility, simulation, arbitrage, option markets, VIX

JEL Classification: G13, G17, C15, C22, C45, C53, C63

Suggested Citation

Vuletić, Milena and Cont, Rama, VolGAN: a generative model for arbitrage-free implied volatility surfaces (October 30, 2023). Available at SSRN: https://ssrn.com/abstract=4617536 or http://dx.doi.org/10.2139/ssrn.4617536

Milena Vuletić (Contact Author)

University of Oxford ( email )

Radcliffe Observatory, Andrew Wiles Building
Woodstock Rd
Oxford, Oxfordshire OX2 6GG
United Kingdom

Rama Cont

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://www.maths.ox.ac.uk/people/rama.cont

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