Exact Terminal Condition Neural Network for American Option Pricing Based on the Black-Scholes-Merton Equations

Battle Count: 84

Highly relevant for quantitative trading as it provides accurate and fast American option pricing, which is essential for derivatives trading desks. The method achieves sub-cent accuracy (MAE ~6x10^-3 for K=100) and fast inference (~1ms per evaluation), making it practical for real-time pricing. Particularly valuable for multi-asset options where traditional methods become computationally infeasible. The free boundary determination capability is directly useful for optimal exercise decisions in trading strategies.

Moderate complexity. The core idea (g1*NN + g2 decomposition) is straightforward, but designing appropriate g2 functions requires understanding of European option analytical solutions, Taylor expansions, and singularity analysis. The loss function with inequality constraints (L_bs, L_tv, L_eq) adds complexity. For multi-asset options, computing bivariate normal CDFs and handling high-dimensional inputs increases implementation difficulty. The input normalization layer and ResNet architecture are standard components. Training requires careful hyperparameter tuning and 200K iterations.

The paper provides detailed network architecture (4-block ResNet, 2 layers, 50 neurons, tanh activation), hyperparameters (Adam optimizer with beta1=0.9, beta2=0.999, lr_start=0.01, gamma=0.9, 200,000 iterations), loss function definitions, sampling strategies, and explicit formulas for g1 and g2 functions. Training domain and evaluation domain are specified. However, no code repository is provided, and some hyperparameter tuning details are experiment-specific. All experiments run on NVIDIA A800 GPU.