Shapley-based Structural Analysis of Neural Calibration for Stochastic Volatility Models

Paper: arXiv 2610.03076

Authors: Shaïn Afzali, Serena Della Corte, Antonis Papapantoleon

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a novel application of Shapley-based XAI methods to understand neural calibration in stochastic volatility models, moving beyond mere predictive accuracy. It combines advanced mathematical concepts from stochastic calculus and neural networks with a rigorous empirical analysis of different architectures and models. The findings offer practical implications for feature selection and model interpretability in quant finance.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand Neural Calibration Mappings for Stochastic Volatility Models] --> B{Methodology: Shapley-based XAI};
    B --> C[Data/Inputs: Heston & Rough Heston Models, Implied Volatility Surface (IVS)];
    C --> D{Computational Process: Train MLP, Highway, Softmax-Highway NNs};
    D --> E[Computational Process: Apply SHAP & $\nu$SHAP for Feature Attribution];
    E --> F[Key Finding 1: Short Maturities & Smile Wings Dominate Parameter Inference];
    F --> G[Key Finding 2: $\nu$SHAP Guides IVS Input Reduction while Maintaining Accuracy];
    G --> H[Outcome: Structural Insight into Learned Mappings & Practical Feature Selection];

Cited References (38)

1. On the nature of ill-posedness of an inverse problem arising in option pricing (2003)
2. A Neural Network-Based Framework for Financial Model Calibration (2019)
3. Deep Calibration with Random Grids — → 2306.11061
4. " W hy S hould I T rust Y ou?": E xplaining the p redictions of a ny c lassifier (2016)
5. Axiomatic Attribution for Deep Networks (2017)
6. On Deep Calibration of (Rough) Stochastic Volatility Models (2025)
7. Analysis of F ourier Transform Valuation Formulas and Applications (2010)
8. The Volatility Surface: A Practitioner’s Guide (2006)

3 of 38 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.