发表机构
Rice University; ENSTA Paris（莱斯大学; 巴黎国立高等先进技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出表面驱动的随机波动率框架，利用CME CVOL数据识别大豆期权波动率微笑中的波动率之波动率与杠杆效应，并通过数值验证支持水平、偏斜和凸性作为动态定价输入。
AI 中文摘要
商品期权曲面包含超出平值波动率水平的信息。我们利用2013年10月至2025年8月的芝加哥商品交易所集团波动率指数（CME CVOL）日度指标，为大豆期货期权开发了一个表面驱动的随机波动率框架。平值水平与凸性为正、右偏，且能很好地由对数Ornstein Uhlenbeck动力学描述，而加性偏斜改变符号，并在实轴上由Ornstein Uhlenbeck过程建模。这些经验特征共同促成了一个均值回归的表面因子系统。在对数OU期货波动率模型下，领先阶微笑关系将平值水平映射到潜在波动率状态，凸性映射到有效的表面隐含波动率的波动率状态，偏斜映射到有效的杠杆状态。我们推导了相关的风险中性定价方程和Feynman Kac表示，通过蒙特卡洛模拟对价格进行基准测试，用有限差分法验证定价偏微分方程，并训练了一个神经网络代理模型以进行快速重复估值。实证结果显示，不同市场体制下表面状态存在显著变化，其中2021年拉尼娜干旱窗口表现出较高的波动率和偏斜度。数值结果显示，在验证网格上，有限差分与蒙特卡洛价格高度一致，而神经网络代理模型以显著更低的推理成本复现了定价映射。总体而言，结果支持将水平、偏斜和凸性联合作为商品期权定价和模型诊断的动态输入。
英文摘要
Commodity option surfaces contain information beyond the at-the-money volatility level. We develop a surface-driven stochastic-volatility framework for soybean futures options using daily Chicago Mercantile Exchange Group Volatility Index (CME CVOL) indicators from October 2013 to August 2025. The ATM level and convexity are positive, right-skewed, and well described by log Ornstein Uhlenbeck dynamics, whereas the additive skew changes sign and is modeled on the real line by an Ornstein Uhlenbeck process. These empirical features motivate a joint mean-reverting surface-factor system. Under a log OU futures volatility model, leading-order smile relations map the ATM level to the latent volatility state, convexity to an effective surface-implied volatility- of-volatility state, and skew to an effective leverage state. We derive the associated risk-neutral pricing equation and Feynman Kac representation, benchmark prices by Monte Carlo simulation, validate the pricing PDE by finite differences, and train a neural-network surrogate for fast repeated valuation. The empirical results show substantial variation in surface states across market regimes, with the 2021 La Nina drought window exhibiting elevated volatility and skewness. The numerical results show close agreement between finite-difference and Monte Carlo prices over the validation grid, while the neural-network surrogate reproduces the pricing map at substantially lower inference cost. Overall, the results support the use of level, skew, and convexity jointly as dynamic inputs for commodity-option pricing and model diagnostics.
