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

2025-01-12

AI Summary

Pricing American options under non-Markovian rough volatility models—such as rough Heston and rough Bergomi—remains challenging due to path-dependent dynamics that violate the Markov assumption. Method: We propose the first dual/primal optimal stopping framework integrating deep signatures with the signature kernel. Our approach abandons the Markov assumption, employs path signatures to capture high-order path dependencies, leverages the signature kernel for efficient kernelized learning, and jointly optimizes upper and lower bounds via deep neural networks. Contribution/Results: This work is the first to systematically incorporate signature theory into American option pricing under non-Markovian dynamics, enabling model-agnostic, unified representation. Experiments demonstrate substantial improvements in convergence speed, numerical stability, and cross-model generalization of bound estimation. The framework establishes a novel paradigm for dynamic hedging and risk measurement in rough volatility environments.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Kernel Methods

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Pricing American options under rough volatility
• Extending signature-based primal and dual solutions
• Comparing performance in rough Heston and Bergomi models

Innovation

• Deep-signature learning for American options
• Signature-kernel methods in non-Markovian frameworks
• Pricing under rough volatility models