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

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "Arbitrage-Aware Probabilistic Multi-Step Forecasting of Implied Volatility Surfaces".

Jane: The gist: A conditional latent diffusion framework for generating joint 30-step trajectories of implied volatility surfaces and underlying returns is proposed to model option market evolution while preserving economic admissibility.

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So we're looking at this paper called "Arbitrage-Aware Probabilistic Multi-Step Forecasting of Implied Volatility Surfaces: Joint Generation of Surface-Return Trajectories Using Latent Diffusion." The main idea here is they want to model how implied volatility surfaces evolve over time, and they need to do it while keeping things economically admissible, meaning no static arbitrage.

Jane: What does that mean for us? So, what's the core claim of this work? Are they just making a prettier picture of the options market or are they actually predicting something useful?

Tom: They propose a conditional latent diffusion framework to generate joint thirty-step trajectories for both the implied volatility surfaces and underlying returns <ref:2608.22478#pg1,propose a conditional latent diffusion framework>. They use an arbitrage-aware autoencoder to learn a low-dimensional representation of the surface, and then a diffusion model captures the evolution of that joint system.

Lu: What's interesting about that structure is how they separate things up: the autoencoder handles representation learning and economic regularization, while the diffusion model takes over for generating the future paths conditional on recent history. That separation is pretty clean.

Meng: From a production standpoint, separating the representation from the generation is good because it means we can potentially update just one part if we need to change how we capture market structure versus how we predict future steps. But what's the actual data setup like?

Lalam: They constructed their data using OptionMetrics data on WRDS from January two thousand to August two thousand twenty-five applying a pretrained three graph neural operator map for each day to get a smooth, essentially static arbitrage-free surface on prescribed coordinates <ref:2608.22478#pg3,a smooth, essentially static arbitrage-free surface on prescribed coordinates>. This results in six thousand four hundred twenty-nine daily t–IVSs and associated conditioning variables <ref:2608.22478#pg3,6429 daily t–IVSs and associated conditioning variables>.

Jane: So it starts with this large dataset spanning over twenty-five years of daily surfaces, and they use that to train the autoencoder part before moving to the diffusion generation part? That sounds like a pretty solid foundation for generating these scenarios.

Tom: Exactly. They then feed the time-scaled surface history along with SPX log returns and rolling summaries of return levels into the diffusion model so it can generate those next thirty days jointly with equity returns in a single pass, conditioned on what happened recently <ref:2608.22478#pg1>.

Meng: One single non-autoregressive pass sounds efficient for generation, but how does that scale up? If we need to run this on live data streams, is that one pass fast enough for real-time forecasting?

Lalam: The results show that the framework generates realistic probabilistic multi-step scenarios on SPX surfaces and also outperforms the persistence benchmark in point forecasting. It generates trajectories that preserve the dominant smile and term-structure geometry, recovering realized level, skew, and curvature factors of surface movements.

Conclusion: Tom: So we've seen how this paper uses a conditional latent diffusion framework to generate joint thirty-step trajectories for implied volatility surfaces and underlying returns <ref:2608.22478#pg1,implied volatility surfaces and underlying returns>. It’s essentially a probabilistic trajectory model rather than just a one-day point forecaster.

Jane: And the authors, Dominik Manuel Buchegger and Lukas Gonon, they are focused on making sure this generation process preserves economic admissibility while capturing the two-dimensional geometry of these surfaces over time.

Lu: The main implication for me is how they handle the arbitrage constraints; they regularized the autoencoder reconstruction map towards no-static–arbitrage consistency, which means admissibility is baked into the representation learning itself rather than just being a post-processing step. That's a key move in representation learning.

Meng: I see them mentioning some limitations in their own work: they found that underdispersion is an issue, meaning the predictive intervals widen with the horizon but remain too narrow, and they also noted weak one-day-ahead performance where persistence is still superior. That tells me this isn't a perfect tool for making super accurate single-step bets right now.

Lalam: The paper shows that while underdispersion is a limitation—the predictive intervals widen with the horizon but remain too narrow—the predictive mean also contains information not available from persistence, and the model overtakes persistence from approximately weekly horizons onward, with gains being strongest at short maturities and in the wings.

Tom: So to wrap up on this paper: they gave us a transparent, reproducible protocol for constructing IVS forecasting datasets from OptionMetrics data on WRDS, allowing licensed users to recreate a common evaluation setting. It's a solid foundation for generating these scenarios.

Jane: It seems like the main contribution is providing this framework for conditional, multi-step generation of joint IVS–return trajectories and evaluating it systematically against persistence, which gives us a benchmark for functional trajectory modeling in this area.