Nonlinear Asian Option Pricing: A Power Series Solution Framework

Abstract

A fundamental challenge in financial mathematics lies in accurately pricing Asian options, especially due to their inherent path dependency. This work introduces a pricing approach for Asian options within a nonlinear Black-Scholes framework utilizing the Power Series Method (PSM). Leveraging the path-dependent nature of Asian options, the PSM approximates the governing nonlinear partial differential equation through a Maclaurin series expansion, enabling recursive computation of coefficients. This method is well-suited for both symbolic and numerical analysis. Numerical experiments demonstrate that the PSM achieves high accuracy and computational efficiency, outperforming traditional methods such as the Explicit Forward Difference Method and Monte Carlo Simulation within specified parameter ranges. These results highlight the PSM’s potential as a robust and efficient tool for pricing complex derivatives in nonlinear market models.