Research on Matrix-Based Algorithm for Binary Tree Model Option Pricing

The binary tree model is a widely utilized method for option pricing in financial engineering. However, traditional algorithms face challenges in computational efficiency and storage demands. This study introduces a matrix-based algorithm for the binary tree model, aiming to enhance the computational process through matrix operations. By transforming the states of binary tree nodes into matrix representations and incorporating recursive computation with matrix operations, this method improves pricing efficiency and simplifies algorithm complexity. Experimental results demonstrate that this approach outperforms traditional methods in execution speed, result accuracy, and storage efficiency, particularly in large-scale computational scenarios. This research provides a novel computational tool for option pricing and lays the groundwork for modeling more complex financial derivatives.