发表机构
CEREMADE, Université Paris Dauphine-PSL; LaMME, Université Évry Paris-Saclay; AIML Global Markets, Barclays（巴黎第九大学-PSL大学CEREMADE研究所; 埃夫里巴黎-萨克雷大学LaMME研究所; 巴克莱银行AIML全球市场部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对局部随机波动率校准的低效问题，提出投影一致神经算子，将昂贵的不动点求解移至离线，在线校准仅需一次算子评估，显著降低延迟并提升了局部波动率和杠杆的预测精度。
AI 中文摘要
局部随机波动率（LSV）结合了普通边际分布与更丰富的微笑动态，但校准需要缓慢、有噪声且序列式的McKean-Vlasov不动点。我们学习一种用于校准三重态的投影一致算子，给定有限报价和随机波动率（SV）骨干，它会联合返回受静态套利约束的隐含波动率曲面、其Dupire局部波动率、LSV杠杆以及投影恒等式所需的条件矩。从期权价格边际出发，我们在对数隐含方差坐标下推导了无除法的Dupire残差，以及Gyöngy投影后的商Fokker-Planck方程。Deep算子网络（DeepONet）和傅里叶神经算子（FNO）实现会强制满足报价拟合、静态套利、Dupire和投影约束。对于证人增强残差系统，我们在LSV存在性和逆残差稳定性下证明了条件识别和经验一致性。在受控合成测试中，远期启动和 Cliquet 误差与粒子方法的差异分别为0.1和0.2个百分点，而校准延迟从98.5毫秒降至0.6毫秒。与测试的基准相比，局部波动率均方根误差（RMSE）降低了36%，杠杆RMSE降低了7%-16%。这些结果支持摊销LSV不动点：昂贵的求解过程移至离线，而在线校准简化为单次投影一致算子评估。
英文摘要
Local-stochastic volatility (LSV) combines vanilla marginals with richer smile dynamics, but calibration requires a slow, noisy and sequential McKean--Vlasov fixed point. We learn a projection-consistent operator for the calibration triple. Given finite quotes and a stochastic-volatility (SV) backbone, it jointly returns an implied-volatility surface subject to static-arbitrage constraints, its Dupire local volatility, LSV leverage and the conditional moment required by the projection identity. Starting from option-price marginals, we derive a division-free Dupire residual in log-implied-variance coordinates and a quotient Fokker--Planck equation after Gyöngy projection. Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO) implementations enforce quote fit, static-arbitrage, Dupire and projection constraints. For the witness-augmented residual system, we prove conditional identification and empirical consistency under LSV existence and inverse residual stability. In controlled synthetic tests, forward-start and cliquet errors differ from a particle method by 0.1 and 0.2 percentage points, while calibration latency falls from 98.5 to 0.6 ms. Compared with the tested baselines, local-volatility root-mean-square error (RMSE) falls by 36% and leverage RMSE by 7-16%. These results support amortizing the LSV fixed point: the expensive solve moves offline, while online calibration reduces to a single projection-consistent operator evaluation.
Comments16 pages, 4 figures, 3 tables
