Simulation of Arbitrage-Free Implied Volatility Surfaces

30 Pages Posted: 10 Jan 2023

See all articles by Rama Cont

Rama Cont

University of Oxford

Milena Vuletić

University of Oxford

Date Written: December 11, 2022


We present a computationally tractable method for simulating arbitrage free implied volatility surfaces. We illustrate how our method may be combined with a factor model for the implied volatility surface to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach conciliates static arbitrage constraints with a realistic representation of statistical properties of implied volatility co-movements. Finally, we introduce VolGAN, a nonparametric generative model for implied volatility surfaces.

Keywords: Implied volatility, scenario simulation, generative models, GAN, volatility modeling, risk management

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

Suggested Citation

Cont, Rama and Vuletić, Milena, Simulation of Arbitrage-Free Implied Volatility Surfaces (December 11, 2022). Available at SSRN: or

Rama Cont

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom


Milena Vuletić (Contact Author)

University of Oxford ( email )

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

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