Forecasting implied volatility surface with generative diffusion models

Diffusion Probabilistic Model (DDPM) for generating one-day-ahead arbitrage-free implied volatility surfaces. To capture the path-dependent nature of volatility dynamics, we condition our model on a set of market variables, including exponentially weighted moving averages (EWMAs) of historical vol-surfaces, returns and squared returns of the underlying asset, and scalar risk indicators associated with the underlying asset. A key challenge is that historical data often contains arbitrage opportunities in the earlier dataset for training, which conflicts with the goal of generating arbitrage-free surfaces. We address this by using a parameter-free weighting scheme based on the signal-to-noise ratio (SNR) to incorporate the arbitrage penalty into the loss function. The scheme dynamically adjusts the penalty strength across the diffusion process. Through numerical experiments using market data, we demonstrate the superior performance of our proposed model in volatility forecasting compared to existing approaches.