Paper: arXiv 2509.05820

Authors: Jayanth Athipatla

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 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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework utilizing rough path theory and Volterra kernels to introduce a dynamic, EWMA-driven Hurst parameter to the rBergomi model. Empirical evaluation is demonstrated across multiple asset classes using Jensen-Shannon distance and derivative pricing, though full code availability details in the excerpt are limited.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Volatility via Time-Dependent Hurst Parameter H_t] --> B[Inputs: Multi-Asset Data<br>Equities, Crypto, Commodities]
    B --> C[Methodology: Continuous EWMA Mechanism<br>Adapts H_t to Instantaneous Variance]
    C --> D[Theory: Unified Rough Differential Equations<br>& Rough Path Framework]
    D --> E[Empirical Validation: Dynamic Fit &<br>Out-of-Sample Pricing]
    E --> F[Findings: Outperforms Constant-Hurst Models,<br>Captures Volatility Clustering & Roughness Bursts]

Cited References (6)

  1. Pricing under rough volatility (2016) — link
  2. Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010)
  3. Empirical properties of asset returns: stylized facts and statistical issues (2001) — link
  4. Volatility is rough (2014) — link
  5. American Option Pricing Under Time-Varying Rough Volatility: A Signature-Based Hybrid Framework (2025) — link
  6. Decoding the ATM Skew with Rough Volatility Models and Machine Learning (2025) — link

0 of 6 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.