Hedging with memory: shallow and deep learning with signatures

TL;DR

This paper explores the use of path signatures in machine learning for hedging exotic derivatives, demonstrating that signature-based features improve performance and efficiency in both deep and shallow learning models under complex volatility dynamics.

Contribution

It introduces signature-based features for hedging in non-Markovian models and compares deep and shallow learning approaches, showing the advantages of signature methods over traditional techniques.

Findings

Signatures outperform LSTMs in neural network hedging tasks.

Signature-based models provide more accurate hedging across various payoffs.

Calibrated signature volatility models yield stable and precise results.

Abstract

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.