Simulation of Arbitrage-Free Implied Volatility Surfaces
30 Pages Posted: 10 Jan 2023
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
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