We introduce a deterministic, policy-targeted Bellman value-iteration framework for computing the optimal exercise boundary of perpetual American put options. Our method replaces path sampling in the Bellman operator with Gauss–Hermite quadrature and employs shape-preserving interpolation for off-grid evaluations, eliminating sampling noise and reducing computational cost. Under the Black–Scholes (BS) model, our approach recovers the analytic boundary with a mean absolute percentage error below 1.5% in approximately 19–56 seconds. The resulting policy values, evaluated via Monte Carlo simulation, deviate from the analytic benchmark by less than 0.07%. For the Heston model, where no closed-form solution exists, our method produces boundaries that differ from a high-resolution finite-difference benchmark by 1–5%. Despite these boundary deviations, the expected payoffs from the policies are remarkably close, with relative policy value gaps well below 0.2%. Notably, our method computes the boundary in about 127–180 seconds, a significant speedup compared to the 2,103–3,119 seconds required by the finite-difference method. This work presents a practical and robust alternative for optimal stopping problems, offering a compelling balance of speed and accuracy, particularly when partial differential equation (PDE) solvers are cumbersome or Monte Carlo simulation is prohibitively expensive.

We propose a neural-network variant integrating the Isolation Forest anomaly detection algorithm into its loss function. By incorporating anomaly scores as weights—effectively treating them as inverse measures of data reliability—the model suppresses outlier impact, yielding modest but consistent accuracy gains. Using KOSPI 200 option price data from 2019 to 2023, our experiments show that this anomaly-based approach enhances predictive accuracy by an average of 4.77% on the test set compared to a baseline neural network. Moreover, performance gains are generally observed across various market conditions, including different moneyness states, trading volumes, and time to maturity. Analysis of the identified anomalies reveals that trading volume and time to maturity are key factors strongly associated with irregularities in option data. Option moneyness also contributes to these irregularity patterns, particularly with other market conditions or at extreme levels. In contrast, interest rates show a less direct impact on anomaly scores in our dataset. These findings are broadly consistent with established market regularities, suggesting the anomaly detector's effectiveness in capturing characteristics of market inefficiencies or challenging pricing conditions. Overall, the proposed methodology contributes to the development of a more robust option pricing framework by better reflecting actual market dynamics. It shows potential during periods of heightened volatility, offering useful insights for further academic and practical applications.