Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

• URL: http://arxiv.org/abs/2608.02778v1
• Date: Mon, 03 Aug 2026 18:21:36 GMT
• Title: Neural Networks with Local Converging Inputs for Efficient Options Pricing Models
• Abstract summary: We present a novel application of Neural Networks with Local ging Inputs (NNLCI) to improve the efficiency of existing numerical methods for pricing multi-asset options.<n>We show that NNLCI significantly reduces computational requirements for high-dimensional problems in real-time options trading and risk management, offering low training costs and strong ability generalization.
• Score: 5.495620491256887
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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