用局部收敛输入神经网络，大幅提升多资产期权定价效率
Neural Networks with Local Converging Inputs for Efficient Options Pricing Models
- 用神经网络修正粗细网格解的局部差异，输入极简
- 测试集误差降低4-12倍，仅需少量训练数据
- 适合实时交易与风险管控中的高维问题
我们提出一种新型神经网络局部收敛输入（NNLCI）方法，用于提升多资产期权定价的数值计算效率。NNLCI采用最简输入格式，显著提升便利性与效率。该方法利用神经网络对粗网格与细网格解进行局部修正，仅需少量高保真训练数据即可实现。我们在一维、二维、三维下的Black-Scholes模型现金或无价值期权，以及Heston随机波动率模型下单资产敲出看涨期权（二维空间为标的价S与瞬时方差v）上验证该方法。结果表明，即便在仅使用部分参数组合训练的情况下，NNLCI仍使细网格数值解的均方根误差（RMSE）降低约4-12倍。这证明了NNLCI能显著降低高维问题的计算需求，适用于实时期权交易与风险管理，具备低训练成本与强泛化能力。
原文摘要 · Abstract (English)
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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