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

Shaïn Afzali; Serena Della Corte; Antonis Papapantoleon

q-fin.CPOct 2, 2026

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

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.

Figures & tables

Panel of Figure 2 — Figure 2.1. Schematic representation of a single highway layer, cf. ( 2.11 ).

	$\kappa$	$\gamma$	$\rho$	$v_{0}$	$\bar{v}$
Lower bound	$0.50$	$0.01$	$-0.95$	$0.0001$	$0.01$
Upper bound	$10.0$	$1.00$	$-0.10$	$0.0400$	$0.20$

Table 4.1. Parameter sampling ranges for the Heston model.

	$\kappa$	$\gamma$	$\rho$	$v_{0}$	$\bar{v}$	$H$
Lower bound	$0.1206$	$0.2720$	$-0.7071$	$0.0262$	$0.0721$	$0.1286$
Upper bound	$0.5041$	$0.3748$	$-0.5940$	$0.0778$	$0.1499$	$0.1766$

Table 4.2. Parameter sampling ranges for the rough Heston model.

Model	Moneyness	Maturity	Features
Heston	$11$ points in $[0.50,\,1.50]$	$8$ points in $[0.10,\,2.00]$	$88$
rough Heston (long)	$9$ points in $[0.60,\,1.40]$	$6$ points in $[0.60,\,2.00]$	$54$
rough Heston (short)	$11$ points in $[0.50,\,1.50]$	$10$ points in $[0.02,\,0.50]$	$110$

Table 4.3. Moneyness–maturity discretisations used throughout the experiments.

Model	Architecture	Parameters	$\kappa$	$\gamma$	$\rho$	$v_{0}$	$\bar{v}$	$H$	Avg. MAE
Heston	MLP ( $2\times 256$ )	89,861	0.0582	0.0089	0.0069	$2.4\mathrm{e}{-4}$	$8.5\mathrm{e}{-4}$	–	0.0150
	HW ( $7\times 64$ )	67,269	0.0346	0.0043	0.0058	$1.1\mathrm{e}{-4}$	$5.2\mathrm{e}{-4}$	–	0.0091
	spHW ( $15\times 64$ )	197,765	0.0307	0.0032	0.0046	$2.1\mathrm{e}{-4}$	$5.8\mathrm{e}{-4}$	–	$\mathbf{0.0079}$
rough Heston (long)	MLP ( $3\times 16$ )	1,526	0.0026	$9.2\mathrm{e}{-4}$	0.0010	$3.7\mathrm{e}{-4}$	$6.8\mathrm{e}{-4}$	$4.2\mathrm{e}{-4}$	0.0010
	HW ( $3\times 64$ )	27,526	0.0064	0.0015	0.0018	$8.7\mathrm{e}{-4}$	0.0014	$7.7\mathrm{e}{-4}$	0.0021
	spHW ( $30\times 64$ )	376,326	0.0011	$4.5\mathrm{e}{-4}$	$3.7\mathrm{e}{-4}$	$2.0\mathrm{e}{-4}$	$3.6\mathrm{e}{-4}$	$2.1\mathrm{e}{-4}$	$\mathbf{4.6\mathrm{e}{-4}}$

Table 4.4. Calibration performance of the considered neural network architectures. For each model, the best-performing configuration of each architecture is reported together with the corresponding parameter count and per-parameter mean absolute errors.

Model	Architecture	IV Surface RMSE (vol. points)
		Mean	Median
Heston	MLP ( $2\times 256$ )	$0.79$	$0.25$
	HW ( $7\times 64$ )	$0.81$	$0.23$
	spHW ( $15\times 64$ )	$\mathbf{0.74}$	$\mathbf{0.19}$
rough Heston (long)	MLP ( $3\times 16$ )	$0.067$	$0.047$
	HW ( $3\times 64$ )	$0.17$	$0.065$

Table 4.5. Implied-volatility surface reconstruction errors of the considered neural network architectures. The mean and median RMSE are computed between the original implied volatility surfaces and the surfaces repriced using the predicted parameter sets. Errors are reported in volatility points, where one volatility point corresponds to one percentage point of implied volatility.

Figure 5.1. Global attribution heatmaps for the Heston model obtained from aggregated SHAP (above) and $\nu$ SHAP (below) explanations using the softmax-parametrized highway architecture.

Figure 5.2. Global attribution heatmaps for the rough Heston model on the long-maturity grid obtained from aggregated SHAP (above) and $\nu$ SHAP (below) explanations using the softmax-parametrized highway architecture.

Figure 5.3. Global attribution heatmaps for the rough Heston model on the short-maturity grid obtained from aggregated SHAP and $\nu$ SHAP explanations using the softmax-parametrized highway architecture.

Figure 5.4. Difference heatmaps between the attribution structures of the softmax-parametrized highway and MLP architectures for the rough Heston long-maturity grid.

Figure 5.5. Comparison of SHAP and $\nu$ SHAP attribution structures for the Hurst parameter $H$ on the rough Heston short-maturity grid.

Figure 5.6. Reduced rough Heston long-maturity grid constructed using the global $\nu$ SHAP attributions. Greyed regions correspond to discarded features, while the retained short-maturity region contains the subset of the implied volatility surface used for retraining the calibration networks.

Grid Type	$\kappa$	$\gamma$	$\rho$	$v_{0}$	$\bar{v}$	$H$	Avg. MAE
Full Grid	0.0011	$4.5\mathrm{e}{-4}$	$3.7\mathrm{e}{-4}$	$2.0\mathrm{e}{-4}$	$3.6\mathrm{e}{-4}$	$2.1\mathrm{e}{-4}$	$4.6\mathrm{e}{-4}$
Reduced Grid	$0.0011$	$3.0\mathrm{e}{-4}$	$3.0\mathrm{e}{-4}$	$1.2\mathrm{e}{-4}$	$3.6\mathrm{e}{-4}$	$1.7\mathrm{e}{-4}$	$\mathbf{3.9\mathrm{e}{-4}}$

Table 5.1. Calibration performance comparison between the original and

\nu

SHAP-guided reduced rough Heston long-maturity grids using the softmax-parametrized highway architecture.

Grid Type	IV Surface RMSE (vol. points)
	Mean	Median
Full Grid	$0.041$	$0.031$
Reduced Grid	$\mathbf{0.026}$	$\mathbf{0.022}$

Table 5.2. Implied volatility surface reconstruction errors for the original and

\nu

SHAPguided reduced rough Heston long maturity grids using the softmax-parametrized highway architecture.

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