# Learning to Detect Symbolic Failure: Machine Learning and the Limits of Black-Scholes

arXiv: https://arxiv.org/abs/2609.27764 · HTML: https://mlsanity.com/paper/2609.27764/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 8 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)

## Abstract (arXiv)

We treat options pricing as a representation problem: can machine learning detect systematic deviations from Black-Scholes using 2.6M real option contracts? We compare three regimes: learned abstract embeddings (Kernel PCA), preserved domain structure (tree-based ensembles), and neural network validation. Tree-based methods outperform kernel dimensionality reduction by 21.5 percentage points (93.8% vs 72.3%), and domain-expert features (Greeks, moneyness) outperform engineered features. NN-based and BS-based deviation labels agree 99.9974% of the time, suggesting deviations reflect market structure rather than model artifact. We conclude that in domains with expert-designed symbolic features, preserving structure beats learning abstractions. We make no claim of exploitable mispricings.