Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

Researchers introduced Neural Networks with Local Converging Inputs (NNLCI), a method that uses a neural network to correct numerical solutions for pricing multi-asset options, reducing root-mean-square error by a factor of 4-12 on test sets. The approach, demonstrated on cash-or-nothing options under the Black-Scholes equation and barrier options under the Heston model, requires minimal high-fidelity training data and lowers computational costs for real-time trading and risk management.

arXiv:2608.02778v1 Announce Type: new Abstract: We present a novel application of Neural Networks with Local Converging Inputs NNLCI to improve the efficiency of existing numerical methods for pricing multi-asset options. The most concise input format for NNLCI has been introduced, offering substantial convenience and efficiency. NNLCI uses a neural network to locally correct solutions from a coarse mesh and a refined mesh relative to the coarse one , 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 one, two, and three spatial dimensions, and on single-asset down-and-out barrier call options under the Heston stochastic-volatility model whose pricing PDE is two-dimensional in the spot price $S$ and the instantaneous variance $v$ . In each case, NNLCI reduces the root-mean-square error RMSE of the refined-mesh numerical solution by a factor of approximately 4-12 on test sets, even when the neural network is trained on only a small subset of parameter combinations. These results demonstrate that NNLCI significantly reduces computational requirements for high-dimensional problems in real-time options trading and risk management, offering low training costs and strong generalization ability.