Operator Deep Smoothing for Implied Volatility

TL;DR

This paper introduces a novel neural operator method for nowcasting implied volatility surfaces, enabling direct, accurate, and arbitrage-consistent smoothing of option data across dynamic market conditions, outperforming traditional neural networks and industry standards.

Contribution

The paper presents a new operator deep smoothing technique using graph neural operators that directly maps raw option data to smoothed implied volatility surfaces, maintaining no-arbitrage constraints and robustness.

Findings

High accuracy on ten years of intraday data

Outperforms classical neural networks and SVI

Maintains no-arbitrage constraints

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.