发表机构
Global Quantitative Modelling & Analytics, DRW（DRW全球量化建模与分析）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于2PI有效作用量和Dyson-Schwinger方程的随机波动率定价框架，通过自洽高斯近似和精确矩生成函数处理微笑，在多种模型下实现高效校准与风险计算。
AI 中文摘要
我们发展了一个非微扰框架，用于随机波动率期权定价，该框架由两粒子不可约（2PI）有效作用量和量子场论的Dyson-Schwinger间隙方程组织。在对数价格、对数波动率或Lamperti坐标中，状态变量的联合分布通过一个自洽高斯分布来近似，其均值和有效扩散由2PI平稳条件得出，漂移雅可比矩阵由统计线性化给出。产生微笑的指数和CEV相互作用通过精确的高斯矩生成函数而非泰勒截断来评估。修饰后的逆传播子是否在时间上是局部的，将马尔可夫模型（其中间隙方程简化为几个常微分方程）与粗糙（Volterra）模型（其中保留完整的双时间传播子，特征函数变为对数方差场上的高斯积分）区分开来。在exp-OU、SABR、粗糙Bergomi和粗糙SABR中，所得确定性引擎与PDE或准蒙特卡洛参考值匹配，误差从亚基点（exp-OU）到个位基点（SABR、粗糙Bergomi）再到数十基点（粗糙SABR），其中粗糙Heston作为可精确变换的对照。以波动率场为条件，远期起始微笑和连续监测障碍简化为仅场的求积，在粗糙Bergomi中直接基于原生Volterra场，因果响应块在一次收缩中给出完整的脉冲vega曲线，其计算量比bump-and-revalue低一到两个数量级。提供了包含完整推导、扩展基准和次要应用（随机利率外汇局部波动率、二次高斯Volterra方差和无套利外汇三角形）的技术补充文件作为附件。
英文摘要
We develop a non-perturbative framework for stochastic-volatility option pricing built on the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables is approximated by a self-consistent Gaussian whose mean and effective diffusion follow from the 2PI stationarity conditions, with the exponential and CEV vertices evaluated through the exact Gaussian moment-generating function rather than a Taylor cut. For exponential vertices the skeletons beyond this level sum in closed form: in exp-OU the evaluated melon level cuts the Hartree error by 20-130x, to 0.01-0.11 bp. Whether the dressed inverse propagator is local in time separates Markovian models, where the gap equation collapses to a few ODEs, from rough (Volterra) models, where the full two-time propagator is retained. At nonzero correlation the field is integrated deterministically by conditioning on its two leading Gaussian modes, with exact conditional moments and a moment-matched law for the integrated variance and leverage integral; in the CEV models the correlated drift enters a Dyson equation around the exact absorbed-CEV propagator, resummed by jumps along the variance clock. These closures match Monte Carlo references for rough Bergomi approximately at their resolution (0.01-0.1 bp) down to H=0.07, rho=-0.9, and price SABR to 0.97 bp over a 72-cell grid with maturities to ten years (75 bp for Hagan's expansion) and rough SABR to 0.92 bp. Conditional on the volatility field, forward-start smiles and continuously-monitored barriers reduce to field-only quadratures on the native Volterra field, and the causal response block yields the impulse-vega curve in one adjoint contraction. Derivations, extended benchmarks and secondary applications are in an ancillary technical supplement.
Comments39 pages, 18 figures, 11 tables. Technical supplement (27 pages) included as an ancillary file. v2: adds deterministic conditional-mode closures and supplement section S11
