Arbitrage-Aware Probabilistic Multi-Step Forecasting of Implied Volatility Surfaces: Joint Generation of Surface-Return Trajectories Using Latent Diffusion

Implied volatility surfaces summarise the option market and are central to many financial applications. Probabilistic forecasting of their future evolution requires modelling two-dimensional geometry, temporal dependence, and predictive uncertainty while preserving economic admissibility. We propose a conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns. An arbitrage-aware autoencoder learns a surface representation, while diffusion captures the evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios. Its predictive mean also outperforms persistence beyond the shortest horizons.