Forecasting implied volatility surface with generative diffusion models

2025-11-10

AI Summary

This paper addresses the tension between minor arbitrage opportunities present in historical implied volatility (IV) surfaces and the strict no-arbitrage requirement of pricing models. To resolve this, we propose a conditional denoising diffusion probabilistic model (DDPM) that jointly incorporates historical IV surfaces, asset returns, and risk indicators. A novel, parameter-free, signal-to-noise-ratio-based dynamic weighting mechanism adaptively modulates the strength of a differentiable no-arbitrage loss during the diffusion process. We theoretically establish that the model converges to a distribution manifold that is both arbitrage-free and faithful to empirical data. Empirical results demonstrate substantial improvements over state-of-the-art GAN-based approaches: the generated IV surfaces more accurately capture stylized features—including leptokurtosis, smile skewness, and curvature—exhibit higher stability across time, and contain virtually no arbitrage opportunities.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We introduce a conditional Denoising Diffusion Probabilistic Model (DDPM) for generating arbitrage-free implied volatility (IV) surfaces, offering a more stable and accurate alternative to existing GAN-based approaches. To capture the path-dependent nature of volatility dynamics, our model is conditioned on a rich set of market variables, including exponential weighted moving averages (EWMAs) of historical surfaces, returns and squared returns of underlying asset, and scalar risk indicators like VIX. Empirical results demonstrate our model significantly outperforms leading GAN-based models in capturing the stylized facts of IV dynamics. A key challenge is that historical data often contains small arbitrage opportunities in the earlier dataset for training, which conflicts with the goal of generating arbitrage-free surfaces. We address this by incorporating a standard arbitrage penalty into the loss function, but apply it using a novel, parameter-free weighting scheme based on the signal-to-noise ratio (SNR) that dynamically adjusts the penalty's strength across the diffusion process. We also show a formal analysis of this trade-off and provide a proof of convergence showing that the penalty introduces a small, controllable bias that steers the model toward the manifold of arbitrage-free surfaces while ensuring the generated distribution remains close to the real-world data.

Problem

• Generating arbitrage-free implied volatility surfaces using diffusion models
• Overcoming historical data arbitrage conflicts with novel penalty weighting
• Capturing volatility dynamics through market variable conditioning

Innovation

• Generative diffusion models for volatility surface forecasting
• Conditioning on market variables for path-dependent dynamics
• Parameter-free arbitrage penalty using signal-to-noise ratio