基于Shapley的随机波动率模型神经校准的结构分析

中文摘要 AI 辅助

基于神经网络的方法已成为传统基于优化的随机波动率模型校准程序的高效替代方案。然而，现有工作主要关注预测精度，对学习得到的逆校准映射结构的理解关注相对较少。在本工作中，我们使用可解释人工智能中互补的基于Shapley的方法，分析了多层感知机、高速公路网络和softmax参数化高速公路架构下Heston和粗糙Heston模型的神经校准映射。具体而言，我们考虑了SHAP和νSHAP解释，它们分别捕捉特征相关性的不同且互补的概念，对应于特征子集的敏感性和充分性。短期期限和微笑翼部始终主导参数推断，且尽管预测精度和参数数量存在差异，主导归因结构在不同架构间保持定性稳定。SHAP与νSHAP之间的参数特定差异进一步揭示了隐含波动率表面的不同区域如何促进参数恢复，并暴露了校准输入中的显著冗余。基于这种冗余，我们表明νSHAP解释可以指导粗糙Heston模型输入维度的显著降低，同时相对于完整隐含波动率表面保持校准精度匹配。这些发现表明，互补的基于Shapley的方法提供了超越预测误差指标的关于学习逆校准映射的结构性洞察，并为神经校准问题中的特征选择提供了实用途径。

英文摘要

Neural network-based approaches have emerged as efficient alternatives to traditional optimization-based procedures for the calibration of stochastic volatility models. However, existing work has focused primarily on predictive accuracy, with comparatively little attention devoted to understanding the structure of the learned inverse calibration mappings. In this work, we analyze neural calibration mappings for the Heston and rough Heston models across multilayer perceptron, highway, and softmax-parametrized highway architectures, using complementary Shapley-based methods from explainable AI. Specifically, we consider SHAP and $ν$SHAP explanations, which capture distinct, complementary notions of feature relevance, corresponding to sensitivity and sufficiency of feature subsets, respectively. Short maturities and smile wings consistently dominate parameter inference, and the dominant attribution structure remains qualitatively stable across architectures despite differences in predictive accuracy and parameter count. Parameter-specific differences between SHAP and $ν$SHAP further reveal how distinct regions of the implied volatility surface contribute to parameter recovery and expose substantial redundancy in the calibration input. Building on this redundancy, we show that $ν$SHAP explanations can guide a significant reduction in input dimensionality for the rough Heston model while matching calibration accuracy relative to the full implied volatility surface. These findings demonstrate that complementary Shapley-based methods provide structural insight into learned inverse calibration mappings beyond predictive error metrics, and offer a practical route to feature selection in neural calibration problems.

发表机构

• TU Delft（代尔夫特理工大学）
• Leiden University（莱顿大学）
• Institute of Applied and Computational Mathematics, FORTH（希腊研究与技术基金会应用与计算数学研究所）

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