Deep learning provides surrogates for computationally intensive interest rate option pricing, but practical deployment requires not only accurate prices but also reliable sensitivities and robustness to regime shifts. We presented a unified, task-driven comparison of a deep operator network (DeepONet), physics-informed neural networks (PINNs), and the deep backward stochastic differential equation (DeepBSDE) for European bond call options under the one-factor Hull–White and two-factor G2++ Gaussian affine term structure models. Using historical US Treasury term structures, we constructed smooth yield curve inputs and sampled broad option/model parameter configurations; closed-form formulas supply reference prices and analytical volatility sensitivities (Vegas). DeepONet was trained by supervised operator learning on price labels, whereas the PINN and DeepBSDE relied solely on partial differential equation (PDE) and backward stochastic differential equation (BSDE) constraints without price supervision. Although training is primarily aligned with pricing, we evaluated out-of-sample price accuracy together with automatic differentiation-based Vega accuracy and price robustness under an out-of-distribution volatility stress test. Across both models, supervised operator learning via DeepONet achieved the highest pricing accuracy on the held-out test set and the highest Vega accuracy, and exhibited the smallest degradation in pricing accuracy under the out-of-distribution volatility stress test.

Financial time-series forecasting requires not only accurate point predictions but also a principled characterization of the uncertainty around future outcomes. We proposed a unified dual-path framework that modeled both forms using a shared variational mode decomposition (VMD) backbone. VMD stabilized nonstationary signals, enabling the predictive path—a long short-term memory (LSTM) network integrated with concrete dropout—to quantify epistemic uncertainty, while the generative path used a conditional Wasserstein generative adversarial network (WGAN) to capture aleatoric risk. Empirical evaluations on the Standard & Poor's 500 (S&P 500) index and Financial Times Stock Exchange 100 (FTSE 100) index demonstrated superior predictive accuracy and distributional fidelity over strong baselines. Comprehensive ablation studies and regime-conditioned analyses revealed a clear frequency-wise division of labor: Low-frequency modes drove predictive accuracy, while the generative path successfully reproduced heavy-tailed, regime-dependent return distributions. These findings underscored the efficacy of decomposed uncertainty modeling for robust financial risk assessment.