Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

Battle Count: 86

The paper directly addresses a core challenge in quantitative trading: fast and accurate pricing of multi-asset and path-dependent options. The NNLCI method reduces computational requirements by 4-12x in RMSE while using minimal training data, making it highly relevant for real-time options trading and risk management. The application to both Black-Scholes (multi-asset) and Heston (stochastic volatility) models covers the most common pricing frameworks used in practice. However, the method is a numerical acceleration technique rather than a trading strategy or market prediction model, so its relevance is to the pricing/valuation infrastructure rather than to alpha generation or portfolio construction directly.

The neural network component is very simple (2 hidden layers, 15-32 neurons, ReLU, Adam optimizer), making the ML part straightforward. However, the full pipeline requires implementing ADI finite-difference solvers for multi-dimensional Black-Scholes and Heston PDEs, constructing nested non-uniform meshes (for Heston), generating reference solutions, and managing parameter grids. The PDE solver infrastructure is the dominant complexity. The singleton patch input format (2-3 inputs) makes the NNLCI integration relatively simple once the numerical solvers are in place.

The paper provides detailed numerical setups including mesh configurations (coarse: 21 nodes, refined: 41 nodes per direction), ADI finite-difference scheme details, parameter grids with exact ranges and discretizations, network architectures (hidden layer sizes, activation functions, optimizer, learning rate, epochs), training/testing gap conventions, and boundary condition treatments. However, no code repository or implementation script is provided. The closed-form Black-Scholes solution is used as ground truth for cash-or-nothing options, and a reference mesh (200x100) is used for Heston model labels, making the experimental pipeline fully specified but requiring reimplementation.