Paper: arXiv 2509.09105

Authors: Yinhao Wu, Ping He

Abstract

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we carry out numerical simulations and option pricing analyses, offering new tools for rough volatility modeling and simulation.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical proof establishing the weak convergence of infinite-lag, score-driven models to rough fractional diffusion processes under heavy-tailed scaling. While theoretically rich and highly novel in bridging discrete observation-driven models with continuous rough volatility, it lacks extensive empirical backtesting on real-world market data within the excerpted theoretical core.

Research Flowchart

  flowchart TD
    A[Goal: Connect Discrete Long-Memory Score-Driven Models to Rough Volatility] --> B[Model Formulation: Score-Driven Models with Infinite-Lag & Heavy-Tailed Decay]
    B --> C[Asymptotic Analysis: Apply High-Frequency Time-Scaling & Limit Theorems]
    C --> D[Key Finding: Weak Convergence to Fractional OU Processes with Hurst H < 1/2]
    D --> E[Applications: New Rough Volatility Models e.g., Limiting EGARCH-infinity]
    E --> F[Numerical Experiments: Simulation Protocols & Option Pricing Analysis]

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2 of 74 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.