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This paper proposes using a generalized Langevin equation (GLE) framework for modeling financial volatility, addressing limitations of fractional Brownian motion (fBm) used in rough volatility models. Unlike fBm which couples memory and scaling properties through a single parameter, the GLE separates these features using distinct components: a memory kernel, potential function, and noise covariance. Empirical tests on public financial datasets reject simplified versions of the model (memoryless leverage effects and time-reversal symmetry) while the rough scaling property itself remains empirically unresolved.
Why it matters
Improved volatility modeling has direct implications for derivative pricing, risk management, and portfolio optimization in financial markets. By decoupling memory from scaling behavior, this framework could enable more accurate forecasting of market volatility patterns and better calibration of option pricing models.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: Borrowed from non-equilibrium statistical mechanics, the generalized Langevin equation (GLE) is imported as a framework for stochastic volatility to address the structural limitations of fractional Brownian motion (fBm), the standard engine of rough volatility. The fBm forces a single parameter to set two logically independent properties at once: how volatility scales and how it remembers. The GLE separates them using a memory kernel $K$, a potential $U$, and a noise covariance $C$. Memory becomes a measurable object, and an asymmetric potential supplies a lever on variance skew that the price-variance correlation cannot reach. Physical-measure tests on public datasets decisively reject two constrained corners of the class, a memoryless leverage effect and time-reversal symmetry, while the central rough scaling constraint is left identification-limited rather than refuted. The paper reports these limits honestly, and validation on industry-grade data remains a valuable direction. The risk-neutral construction and the joint SPX–VIX calibration will be developed in a companion paper.
Source: Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation