将非弹性市场校准至期权：Lean Marketron模型与广义朗之万方程
Calibrating Inelastic Markets to Options: The Lean Marketron and the Generalized Langevin Equation
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中文总结 AI 辅助
本文针对Marketron模型的不可识别问题，提出九参数简化模型，将其校准至SPX期权，推导得到含记忆核的广义朗之万方程，验证市场处于驱动非平衡态。
中文摘要 AI 辅助
文献\uc110HalperinItkin2025Mark\uc111中的Marketron模型及其期权定价扩展文献\uc110HalperinItkinMarketron2\uc111存在结构不可识别问题：十八参数空间会将求解器困在次优局部极小值中，导致经济量无法测量。通过移除精确标度规范与符号对称性、按显式准则冻结非金融参数、绝热消除快速隐藏信号，我们推导得到稳健的九参数简化模型。具有空零空间的高斯-牛顿海森矩阵与流形边界分析证实，简化核心无精确对称性且无法进一步简化。资金流与收益创新间的扩散相关性捕捉了短期期权的偏斜特征。针对SPX期权，从物理测度到风险中性测度的分阶段校准用单一参数集拟合了整个期权曲面。该简化还将资金流块的物理值与定价值之间的楔角转化为定义明确的资金流风险市场价格，而非脊状伪影，这是首次实现该量的可识别性，不过单一期权曲面仅能对其水平施加较弱约束。最后，我们的分析表明，Marketron模型中的对数价格服从带有闭式、状态调制记忆核的广义朗之万方程，且记忆变量本身是该核的精确马尔可夫提升。该映射还产生了可检验条件：信号与记忆的弛豫率相等，在SPX曲面上二者分离度较高，但均识别度较弱，这使得拟合的市场暂处于驱动非平衡态，将活性物质类比从隐喻转化为可证伪约束。
英文摘要
The Marketron model of \cite{HalperinItkin2025Mark} and its option pricing extension in \cite{HalperinItkinMarketron2} suffer from structural non-identifiability: an eighteen-parameter space traps solvers in suboptimal local minima and renders economic quantities unmeasurable. By removing exact scaling gauges and sign symmetries, freezing non-financial parameters by explicit criteria, and adiabatically eliminating the fast hidden signal, we derive a robust nine-parameter reduced model. A Gauss-Newton Hessian with empty null space and a manifold-boundary analysis confirm that the reduced core carries no exact symmetry and admits no further reduction. A diffusive correlation between flow and return innovations captures the short-maturity skew. A staged calibration from the physical measure to the risk-neutral measure, illustrated on SPX options, fits the whole surface with a single parameter set. The same reduction turns the wedge between the physical and pricing values of the flow block into a well-defined market price of flow risk rather than a ridge artifact, identifiable here for the first time, though a single surface constrains its level only weakly. Finally, our analysis reveals that in the Marketron model the log-price obeys a generalized Langevin equation with a closed-form, state-modulated memory kernel, and that the memory variable itself is the exact Markovian lift of this kernel. This mapping also yields a testable condition, the equality of the signal and memory relaxation rates, which on the SPX surface come out well separated, though both weakly identified, placing the fitted market tentatively in the driven, non-equilibrium regime and turning the active-matter reading from an analogy into a falsifiable constraint.
