Simulation of Arbitrage-Free Implied Volatility Surfaces

Abstract

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