Arbitrage-Aware Probabilistic Multi-Step Forecasting of the Implied Volatility Surface: Jointly Generating Surface-Return Trajectories with Latent Diffusion

The study proposes a conditional latent diffusion framework that jointly generates 30-step trajectories of the implied volatility surface and underlying returns. It learns surface representations through an arbitrage-aware autoencoder, with the diffusion process capturing the evolution dynamics. The framework is evaluated on the SPX surface dataset and can generate realistic probabilistic multi-step scenarios, with its forecast mean outperforming the persistence benchmark for horizons beyond the shortest maturity.