发表机构
University of Leicester; Toronto Metropolitan University（莱斯特大学; 多伦多都会大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在连续时间等价鞅测度框架下，通过补偿随机指数表示将边际效用加权转化为真鞅密度，并实证检验其作为密度比率可容许性检验优于SVI。
AI 中文摘要
本文将Samuelson-Merton的“效用概率”构造和基于偏好的状态价格解释置于连续时间等价鞅测度框架内。其贡献不在于边际效用定价核的存在性，而在于“效用概率”密度的补偿随机指数表示。只有在风险厌恶和谨慎产生的漂移被补偿后，通过边际效用进行的行为加权才成为等价鞅测度。在正性、可积性、归一化和鞅条件下，行为密度由布朗核$-A_t\sigma_t$生成，其中$A_t$是Arrow-Pratt风险态度，$\sigma_t$是状态波动率。所需的补偿器识别出有限变差项，该项必须在边际效用加权定义真正的鞅密度之前被移除。该框架在共同可容许核下保持看跌-看涨平价，并通过波动率暴露得出连接期权与标的资产溢价的Cox-Ross风险溢价恒等式。在实证方面，本文将期权隐含密度和物理密度映射为带符号的Arrow-Pratt分解，其中正曲率解释为风险厌恶，负曲率解释为风险寻求或投机倾向。在流动性指数ETF和单名期权面板中，当两个模型接受相同的总方差正性和蝶形密度惩罚时，套利惩罚的EBMM的池化留出平方误差损失低于套利惩罚的SVI，尽管切片层面的结果仍好坏参半。该练习最好被解读为密度比率可容许性检验，而非生产性波动率曲面估计的替代品。
英文摘要
The paper places the Samuelson--Merton ``util-prob'' construction and preference-based state-price interpretation inside a continuous-time equivalent-martingale-measure framework. The contribution is not the existence of a marginal-utility pricing kernel, but a compensated stochastic-exponential representation of the ``util-prob'' density. Behavioral weighting by marginal utility becomes an equivalent martingale measure only after the drift generated by risk aversion and prudence is compensated. Under positivity, integrability, normalization, and martingale conditions, the behavioral density is generated by the Brownian kernel $-A_tσ_t$, where $A_t$ is Arrow--Pratt risk attitude and $σ_t$ is state volatility. The required compensator identifies the finite-variation term that must be removed before marginal-utility weighting defines a true martingale density. The framework preserves put--call parity under a common admissible kernel and yields a Cox--Ross risk-premium identity linking option and underlying premia through volatility exposures. Empirically, the paper maps option-implied and physical densities into a signed Arrow--Pratt decomposition, with positive curvature interpreted as risk aversion and negative curvature as risk-seeking or speculative tilt. In a panel of liquid index ETF and single-name options, arbitrage-penalized EBMM has lower pooled holdout squared-error loss than arbitrage-penalized SVI when both models receive the same total-variance positivity and butterfly-density penalties, although slice-level results remain mixed. The exercise is best read as a density-ratio admissibility test rather than a replacement for production volatility-surface estimation.
