Generalization of the residual neural network option pricer to extreme price regimes

Determine whether the residual deep neural network trained on Petrobras European call options generalizes to extreme pricing scenarios—specifically, options with premiums outside the 3–19 BRL range—and rigorously characterize its predictive accuracy and error behavior under such conditions to assess robustness beyond the range where it currently outperforms the Black–Scholes model.

Background

The paper trains a residual neural network to predict Petrobras European call option prices and compares it against the Black–Scholes model. The model achieves a 64.3% reduction in mean absolute error within the 3–19 BRL price range, covering roughly 43.41% of Petrobras option transactions in the test set.

However, the authors note that the neural network tends to overestimate prices outside the 3–19 BRL range. They further state that, despite improved accuracy for longer expiration periods, the model’s generalization to extreme pricing scenarios remains unresolved, indicating a gap in robustness beyond the well-performing range.