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

TL;DR

This paper introduces ETCNN, a deep learning approach that precisely solves the Black-Scholes-Merton equations for American option pricing, ensuring exact terminal conditions and handling non-smooth behaviors.

Contribution

The paper presents ETCNN, a novel neural network framework that guarantees exact terminal conditions and effectively manages non-smooth features in American option pricing.

Findings

Achieves high accuracy in American option pricing.

Outperforms traditional numerical and machine learning methods.

Demonstrates robustness across various scenarios.

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.