Neural Networks with Local Converging Inputs for Efifcient Options Pricing Models
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摘要
We present a novel application of Neural Networks with Local Converging Inputs (NNLCI) to improve the efficiency of existing numerical methods for pricing multiasset options. NNLCI uses a neural network to locally correct solutions from a coarse mesh and a refined mesh, requiring only a minimal amount of high-fidelity training data. We demonstrate this approach on cash-or-nothing options under the Black–Scholes equation in 1D, 2D, and 3D, and on single-asset down-and-out barrier calls under the Heston stochastic-volatility model (PDE is two-dimensional in S and v). NNLCI reduces RMSE of the refined-mesh solution by about 4–12× on test sets, even with training on a small subset of parameter combinations, highlighting substantial reductions in computational cost and strong generalization for real-time pricing and risk management [page::1].
