# Hedging with memory: shallow and deep learning with signatures

arXiv: https://arxiv.org/abs/2508.02759 · HTML: https://mlsanity.com/paper/2508.02759/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 3 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Neural networks for option pricing and hedging: a literature review](https://mlsanity.com/paper/1911.05620/) (2019)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)
- [Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition](https://mlsanity.com/paper/1610.02616/) (2016)
- [A signature-based machine learning model for bipolar disorder and borderline personality disorder](https://mlsanity.com/paper/1707.07124/) (2017)
- [Deep Hedging under Rough Volatility](https://mlsanity.com/paper/2102.01962/) (2021)
- [SigFormer: Signature Transformers for Deep Hedging](https://mlsanity.com/paper/2310.13369/) (2023)
- [Signature Trading: A Path-Dependent Extension of the Mean-Variance Framework with Exogenous Signals](https://mlsanity.com/paper/2308.15135/) (2023)
- [Application of the Signature Method to Pattern Recognition in the CEQUEL Clinical Trial](https://mlsanity.com/paper/1606.02074/) (2016)

## Built on by (most cited first, 3 of 3)

- [The Volterra signature](https://mlsanity.com/paper/2603.04525/) (2026)
- [Tradable Ito Signatures: A Model-Free, Interpretable Framework for Dynamic Hedging](https://mlsanity.com/paper/2608.18120/) (2026)
- [Deep kernel hedging](https://mlsanity.com/paper/2609.34474/) (2026)

## Abstract (arXiv)

We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural networks and show that they outperform LSTMs in most cases, with orders of magnitude less training compute. In a shallow learning setting, we compare two regression approaches: the first directly learns the hedging strategy from the expected signature of the price process; the second models the dynamics of volatility using a signature volatility model, calibrated on the expected signature of the volatility. Solving the hedging problem in the calibrated signature volatility model yields more accurate and stable results across different payoffs and volatility dynamics.