用动态赫斯特参数建模波动率，更好捕捉市场剧烈变化。
Volatility Modeling via EWMA-Driven Time-Dependent Hurst Parameters
- 用实时波动率驱动的指数加权平均法动态调整赫斯特参数。
- 在股票、加密货币和大宗商品上均显著提升定价准确性。
- 基于粗糙路径理论保证数学严谨性，适合量化研究者使用。
我们提出一种新型粗糙伯格米模型，其赫斯特参数 $H_t$ 由方差驱动的指数加权移动平均（EWMA）机制动态决定，与现有机器学习和小波方法有本质区别。该框架首次建立统一的粗糙微分方程（RDE）形式，基于粗糙路径理论，使赫斯特参数能通过连续的EWMA机制随即时波动率演变，从而捕捉波动聚集和粗糙突发现象。不同于离散模式切换或计算复杂的预测方法，本方法兼具数学可处理性与高精度。我们严格证明了解的存在性与唯一性，并推导出鞅性质。在股票、加密货币及商品等多类资产上的实证验证表明，该模型在捕捉动态特征和外样本定价方面表现优异，显著优于传统恒定赫斯特参数模型。
原文摘要 · Abstract (English)
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.
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