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 νSHAP 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 νSHAP 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 νSHAP 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
Figure 2.1. Schematic representation of a single highway layer, cf. ( 2.11 ).
Figure 2.2. Schematic representation of a single softmax-parametrized highway layer, cf. ( 2.12 ), ( 2.13 ).
κ
γ
ρ
v0
vˉ
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.
κ
γ
ρ
v0
vˉ
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
κ
γ
ρ
v0
vˉ
H
Avg. MAE
Heston
MLP ( 2×256 )
89,861
0.0582
0.0089
0.0069
2.4e−4
8.5e−4
–
0.0150
HW ( 7×64 )
67,269
0.0346
0.0043
0.0058
1.1e−4
5.2e−4
–
0.0091
spHW ( 15×64 )
197,765
0.0307
0.0032
0.0046
2.1e−4
5.8e−4
–
0.0079
rough Heston (long)
MLP ( 3×16 )
1,526
0.0026
9.2e−4
0.0010
3.7e−4
6.8e−4
4.2e−4
0.0010
HW ( 3×64 )
27,526
0.0064
0.0015
0.0018
8.7e−4
0.0014
7.7e−4
0.0021
spHW ( 30×64 )
376,326
0.0011
4.5e−4
3.7e−4
2.0e−4
3.6e−4
2.1e−4
4.6e−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 ( 2×256 )
0.79
0.25
HW ( 7×64 )
0.81
0.23
spHW ( 15×64 )
0.74
0.19
rough Heston (long)
MLP ( 3×16 )
0.067
0.047
HW ( 3×64 )
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 ν 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 ν 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 ν 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 ν 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 ν 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
κ
γ
ρ
v0
vˉ
H
Avg. MAE
Full Grid
0.0011
4.5e−4
3.7e−4
2.0e−4
3.6e−4
2.1e−4
4.6e−4
Reduced Grid
0.0011
3.0e−4
3.0e−4
1.2e−4
3.6e−4
1.7e−4
3.9e−4
Table 5.1. Calibration performance comparison between the original and ν 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
0.026
0.022
Table 5.2. Implied volatility surface reconstruction errors for the original and ν SHAPguided reduced rough Heston long maturity grids using the softmax-parametrized highway architecture.