发表机构
Tandon School of Engineering, New York University（纽约大学坦登工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入广义朗之万方程作为随机波动率框架，解耦记忆与标度，克服分数布朗运动的局限，并通过物理测度检验揭示杠杆效应与时间反演对称性被拒绝，而粗糙标度约束仅受识别限制。
AI 中文摘要
借鉴非平衡统计力学，广义朗之万方程（GLE）被引入作为随机波动率的框架，以解决分数布朗运动（fBm）——粗糙波动率的标准引擎——的结构性局限。fBm迫使单一参数同时设定两个逻辑上独立的性质：波动率如何标度以及它如何记忆。GLE通过记忆核$K$、势$U$和噪声协方差$C$将二者分离。记忆成为可测量的对象，而非对称势为价格-方差相关性无法触及的方差偏斜提供了杠杆。在公开数据集上的物理测度检验明确拒绝了该类的两个受限角落，即无记忆杠杆效应和时间反演对称性，而核心的粗糙标度约束则因识别限制而未被反驳，而非被证伪。论文如实报告了这些限制，对行业级数据的验证仍是一个有价值的方向。风险中性构建以及SPX-VIX联合校准将在配套论文中展开。
英文摘要
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.
Comments44 pages, 8 tables, 4 figures
