Pricing American options under rough volatility using deep-signatures and signature-kernels

TL;DR

This paper introduces deep-signature and signature-kernel methods to improve the pricing of American options in non-Markovian rough volatility models, extending previous signature-based solutions.

Contribution

It integrates deep-signature and signature-kernel learning into primal and dual optimal stopping solutions for non-Markovian models, enabling effective American option pricing under rough volatility.

Findings

Effective pricing of American options under rough Heston and Bergomi models.

Comparison shows improved performance over existing methods.

Extension of signature-based optimal stopping to non-Markovian frameworks.

Abstract

We extend the signature-based primal and dual solutions to the optimal stopping problem recently introduced in [Bayer et al.: Primal and dual optimal stopping with signatures, to appear in Finance & Stochastics 2025], by integrating deep-signature and signature-kernel learning methodologies. These approaches are designed for non-Markovian frameworks, in particular enabling the pricing of American options under rough volatility. We demonstrate and compare the performance within the popular rough Heston and rough Bergomi models.