Volatility Modeling via EWMA-Driven Time-Dependent Hurst Parameters
This work addresses volatility modeling for financial practitioners, offering a mathematically tractable alternative to existing methods, though it appears incremental as it builds on rough Bergomi models with a novel parameter adaptation mechanism.
The paper tackles the problem of modeling volatility in financial markets by introducing a rough Bergomi model with a time-dependent Hurst parameter driven by an exponentially weighted moving average, which adapts to volatility regimes and shows superior performance in capturing dynamics and pricing accuracy across asset classes like equities and cryptocurrencies.
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 existence and uniqueness of solutions via rough path theory and derive martingale properties. Empirical validation on 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.