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

ArXiv ID: 2510.27132 “View on arXiv”

Authors: Wenxuan Zhang, Yixiao Guo, Benzhuo Lu

Abstract

This paper proposes the Exact Terminal Condition Neural Network (ETCNN), a deep learning framework for accurately pricing American options by solving the Black-Scholes-Merton (BSM) equations. The ETCNN incorporates carefully designed functions that ensure the numerical solution not only exactly satisfies the terminal condition of the BSM equations but also matches the non-smooth and singular behavior of the option price near expiration. This method effectively addresses the challenges posed by the inequality constraints in the BSM equations and can be easily extended to high-dimensional scenarios. Additionally, input normalization is employed to maintain the homogeneity. Multiple experiments are conducted to demonstrate that the proposed method achieves high accuracy and exhibits robustness across various situations, outperforming both traditional numerical methods and other machine learning approaches.

Keywords: American options, Deep Learning, Black-Scholes-Merton, neural network, finite differences

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper demonstrates high mathematical complexity through its derivation of the Exact Terminal Condition Neural Network (ETCNN) and adaptation of the Black-Scholes-Merton equations, and shows strong empirical rigor by conducting extensive experiments comparing ETCNN to traditional and other ML methods, demonstrating high accuracy and robustness.

  flowchart TD
    A["Research Goal: Accurate American Option Pricing"] --> B{"Methodology: Exact Terminal Condition Neural Network"}
    B --> C["Input Data: BS-Merton Equation Parameters"]
    C --> D["Neural Network Architecture"]
    D --> E["Key Innovation: Terminal Constraint Function"]
    E --> F["Training with Homogeneity-Preserving Normalization"]
    F --> G["Output: Robust & Accurate Option Prices"]
    G --> H["Outcome: Outperforms Finite Differences & ML Baselines"]