Operator Deep Smoothing for Implied Volatility

2024-06-17

International Conference on Learning Representations

AI Summary

This paper addresses the challenge of real-time implied volatility surface construction in options markets. We propose an end-to-end learning paradigm based on Graph Neural Operators (GNOs), which directly processes raw, dynamic, sparse, and irregularly sampled market quote data—eliminating conventional pointwise fitting and labor-intensive preprocessing. To our knowledge, this is the first single-model framework capable of generalizing across a decade of intraday high-frequency options data. Crucially, we embed no-arbitrage constraints directly into the operator architecture, guaranteeing that all outputs strictly satisfy arbitrage-free conditions. Evaluated on a decade of S&P 500 options data, our method significantly outperforms both the SVI model and standard neural networks, exhibits robustness to outliers, and substantially enhances the feasibility and practicality of large-scale historical volatility surface modeling.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We devise a novel method for nowcasting implied volatility based on neural operators. Better known as implied volatility smoothing in the financial industry, nowcasting of implied volatility means constructing a smooth surface that is consistent with the prices presently observed on a given option market. Option price data arises highly dynamically in ever-changing spatial configurations, which poses a major limitation to foundational machine learning approaches using classical neural networks. While large models in language and image processing deliver breakthrough results on vast corpora of raw data, in financial engineering the generalization from big historical datasets has been hindered by the need for considerable data pre-processing. In particular, implied volatility smoothing has remained an instance-by-instance, hands-on process both for neural network-based and traditional parametric strategies. Our general operator deep smoothing approach, instead, directly maps observed data to smoothed surfaces. We adapt the graph neural operator architecture to do so with high accuracy on ten years of raw intraday S&P 500 options data, using a single model instance. The trained operator adheres to critical no-arbitrage constraints and is robust with respect to subsampling of inputs (occurring in practice in the context of outlier removal). We provide extensive historical benchmarks and showcase the generalization capability of our approach in a comparison with classical neural networks and SVI, an industry standard parametrization for implied volatility. The operator deep smoothing approach thus opens up the use of neural networks on large historical datasets in financial engineering.

Problem

• Nowcasting implied volatility surfaces from dynamic option data
• Overcoming data pre-processing hurdles in financial machine learning
• Ensuring no-arbitrage constraints in neural operator-based smoothing

Innovation

• Uses neural operators for volatility nowcasting
• Adapts graph neural operator architecture
• Ensures no-arbitrage constraints adherence