We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black--Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over
(S,t). The model embeds the BS operator and boundary/terminal conditions in a residual-based objective and requires no labeled prices. For American options, early exercise is handled via an obstacle-style relaxation while retaining the BS residual in the continuation region. To quantify \emph{epistemic} uncertainty, we introduce an anchored-ensemble fine-tuning stage (AT--PINN) that regularizes each model toward a sampled anchor and yields prediction bands alongside point estimates. On European calls/puts, the approach attains low errors (e.g., MAE
∼5×10−2, RMSE
∼7×10−2, explained variance
≈0.999 in representative settings) and tracks ground truth closely across strikes and maturities. For American puts, the method remains accurate (MAE/RMSE on the order of
10−1 with EV
≈0.999) and does not exhibit the error accumulation associated with time-marching schemes. Against data-driven baselines (ANN, RNN) and a Kolmogorov--Arnold FINN variant (KAN), our PINN matches or outperforms on accuracy while training more stably; anchored ensembles provide uncertainty bands that align with observed error scales. We discuss design choices (loss balancing, sampling near the payoff kink), limitations, and extensions to higher-dimensional BS settings and alternative dynamics.