ANALYZING THE AMERICAN PORTFOLIO OPTIONS WITHIN THE CEV MODEL INCORPORATING DIVIDEND YIELD BY THE LIE SYMMETRY APPROACH

This study aims to use the classical Lie symmetry algorithm to solve a mathematical model that represents the American put option. The model is based on a constant elasticity of variance (CEV) framework and includes factors like dividend yield. An infinitesimal transformation and symmetry generators are obtained for the governing parabolic (1+1) PDE which is also known as a price equation. Classical symmetries for the Black Scholes, Cox-Ingersoll-Ross, and general CEV models with dividend yield help us understand the mathematical structure of these models and their relationships, enabling us to develop more accurate pricing models and better understand investment risks. Group invariant solutions of governing PDE are obtained by using similarity variables which are evaluated by solving the characteristic equation of the symmetry operator. A graphical representation of solutions with different dividend yields is presented and discussed to identify the new attribute. The results indicate that rising interest rates, volatility, dividends, and expiration time conform to the established trends. The effects of the dividends yield in all three cases show a high premium value.