American Option Pricing Under Time-Varying Rough Volatility: A Signature-Based Hybrid Framework

TL;DR

This paper presents a flexible, signature-based hybrid framework for American option pricing that dynamically adapts to changing volatility roughness, improving accuracy and computational efficiency in real-time market conditions.

Contribution

It introduces a novel hybrid approach combining dynamic Hurst parameter estimation, regime switching, and efficient kernel evaluations for improved American option pricing.

Findings

Roughness assumption often violated during stable markets

Hybrid framework improves pricing accuracy over fixed-roughness models

Reduces computational cost while maintaining accuracy

Abstract

We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate the time-varying Hurst parameter H(t) from rolling windows of recent volatility data. Second, we feed these forecasts into a regime switch that chooses either a rough Bergomi or a calibrated Heston simulator, depending on the predicted roughness. Third, we accelerate signature-kernel evaluations with Random Fourier Features (RFF), cutting computational cost while preserving accuracy. Empirical tests on S&P 500 equity-index options reveal that the assumption of persistent roughness is frequently violated, particularly during stable market regimes when H(t) approaches or exceeds 0.5. The proposed hybrid framework provides a flexible structure that adapts to changing volatility roughness, improving performance over fixed-roughness baselines and reducing duality gaps in some regimes. By integrating a dynamic Hurst parameter estimation pipeline with efficient kernel approximations, we propose to enable tractable, real-time pricing of American options in dynamic volatility environments.