Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

2026-08-03

AI Summary

This study addresses the high computational cost and low efficiency inherent in pricing high-dimensional financial derivatives, particularly in real-time trading and risk management. The authors propose a neural network approach based on locally convergent inputs (NNLCI), which integrates coarse-to-fine grid numerical solutions of partial differential equations from the Black–Scholes and Heston models and corrects local errors using only a minimal amount of high-fidelity data. Requiring only compact input representations and a small number of training samples, the method substantially improves pricing accuracy for multi-asset options. Empirical results demonstrate a 4–12× reduction in test-set root mean squared error (RMSE) across one- to three-dimensional problems, achieving strong generalization while significantly alleviating the computational burden typically associated with high-dimensional derivative pricing.

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.

Problem

• options pricing
• numerical methods
• high-dimensional problems
• computational efficiency
• multi-asset options

Innovation

• Neural Networks with Local Converging Inputs
• options pricing
• mesh refinement
• high-dimensional PDEs
• computational efficiency