Document Type : Research Article

Author

• Jayanth Athipatla

19316 Williams Street

Abstract

We introduce a novel rough Bergomi (rBergomi) model featuring a variance-driven exponentially weighted moving average (EWMA) time-dependent Hurst parameter $H_t$, fundamentally distinct from recent machine learning and wavelet-based approaches in the literature. Our framework pioneers a unified rough differential equation (RDE) formulation grounded in rough path theory, where the Hurst parameter dynamically adapts to evolving volatility regimes through a continuous EWMA mechanism tied to instantaneous variance. Unlike discrete model-switching or computationally intensive forecasting methods, our approach provides mathematical tractability while capturing volatility clustering and roughness bursts. We rigorously establish the existence and uniqueness of solutions via rough path theory and derive martingale properties. Empirical validation in diverse asset classes including equities, cryptocurrencies, and commodities demonstrates superior performance in capturing dynamics and out-of-sample pricing accuracy. Our results show significant improvements over traditional constant-Hurst models.

Keywords

• Stochastic
• Volatility
• Hurst
• Rough