Analytical solution to the Black-Scholes Equation: Adomian Decomposition Method Versus Lie Algebraic Approach

Abstract

In this paper, we compare two relevant methods to find Analytical solution of the Black-Scholes Equation. First, we apply the Adomian Decomposition Method as in [2], to obtain a solution to the aforementioned equation with boundary condition for a European option. Secondly, we apply the Lie algebraic Approach for determining the solution as in [7]. Those two methods conducted us to investigate the thin line between the underlying results. Finally, we suggest a simple enhanced Due Diligence on both approaches.

Keywords

• black-scholes equation
• adomian decomposition method
• lie algebraic approach
• symmetry analysis.