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

Roshan Shah

Papers from arXiv.org

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.

Date: 2025-08, Revised 2025-08
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