Arbitrage-Aware Multi-Step Forecasting of Implied Volatility Surfaces: Modelling Surface Trajectories Using Latent Diffusion

Abstract:Implied volatility surfaces summarise the option market and are central to many financial applications. Forecasting 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 low-dimensional surface representation, while the diffusion model captures the conditional joint evolution. Evaluated on SPX surfaces, the framework generates realistic probabilistic multi-step scenarios while also outperforming the persistence benchmark in point forecasting.

Mathematical Finance (q-fin.MF); Machine Learning (cs.LG)

arXiv:2608.22478 [q-fin.MF]

(or arXiv:2608.22478v1 [q-fin.MF] for this version)

https://doi.org/10.48550/arXiv.2608.22478 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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