Predicting Implied Volatility Surfaces with Generative Diffusion Models

The study proposes a conditional denoising diffusion probabilistic model (DDPM) for generating next-day approximately arbitrage-free implied volatility surfaces. The model is conditioned on the exponentially weighted moving average of historical volatility surfaces, underlying asset returns, squared returns, and related risk indicators, and incorporates arbitrage penalties into the loss function through a signal-to-noise ratio (SNR)-based weighting scheme. Numerical experiments based on S&P 500 options market data show that the model outperforms existing modern and classical methods in volatility forecasting.