Simulating Arbitrage-Free Implied Volatility Surfaces

We present a computationally tractable method for simulating arbitrage free implied volatility surfaces. Our approach conciliates static arbitrage constraints with a realistic representation of statistical properties of implied volatility co-movements.
We illustrate our method with two examples. First, we propose a dynamic factor model for the implied volatility surface, and show how our method may be used to remove static arbitrage from model scenarios. As a second example, we propose a nonparametric generative model for implied volatility surfaces based on a Generative Adversarial Network (GAN).