# Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction

arXiv: https://arxiv.org/abs/1904.12834 · HTML: https://mlsanity.com/paper/1904.12834/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2019.

## Built on by (most cited first, 7 of 7)

- [A Survey of Explainable Artificial Intelligence (XAI) in Financial Time Series Forecasting](https://mlsanity.com/paper/2407.15909/) (2024)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs](https://mlsanity.com/paper/2303.00859/) (2023)
- [Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications](https://mlsanity.com/paper/2604.00987/) (2026)
- [A Geometry-Aware Residual Correction of Hagan's SABR Implied Volatility Formula](https://mlsanity.com/paper/2605.06604/) (2026)
- [ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.02117/) (2026)
- [Neural Slack Variables for Shape Constraints](https://mlsanity.com/paper/2606.13803/) (2026)

## Abstract (arXiv)

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.