NISE: Neural-Informed Shrinkage Estimation for High-Dimensional Derivative Pricing under Financial Models

High-dimensional derivative pricing commonly relies on Monte Carlo (MC) simulation or neural partial differential equation (PDE) solvers. However, MC methods may require a large simulation budget to achieve low estimation error, while neural predictions may become inaccurate under distribution shift. To address these limitations, we propose Neural-Informed Shrinkage Estimation (\NISE), a hybrid pricing method that uses predictions from an independently trained neural PDE solver as shrinkage targets in a James–Stein estimator. MC samples determine the shrinkage strength, allowing the estimator to exploit informative neural predictions while reducing their influence when they disagree with simulated prices. On the theoretical side, we establish strict dominance over MC under Gaussianity. We then extend the analysis beyond the Gaussian setting and derive a finite-sample risk bound under mild assumptions. The bound explicitly depends on prediction accuracy and yields an $O(N^{-1/4})$ upper bound on the excess risk relative to MC, where $N$ denotes the simulation budget; moreover, when the MC budget and neural prediction accuracy lie within an appropriate regime, we recover strict dominance over MC without assuming Gaussianity. On the empirical side, experiments on basket options, credit default swaps (CDS), and option pricing under a Heston model calibrated to real-world market data demonstrate performance improvements.