Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation
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.
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BibTeX
@misc{itkin2026beyond,
title = {{Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation}},
author = {Andrey Itkin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20293},
eprint = {2609.20293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20293},
}
RIS
TY - UNPB
TI - Beyond Rough Volatility: Decoupling Memory and Scaling via a Generalized Langevin Equation
AU - Andrey Itkin
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20293
UR - https://arxiv.org/abs/2609.20293
AB - 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.
ER -