TITLE:
Numerical Solutions of the Black-Scholes Financial Model Using the Adomian Decomposition and Power Series Collocation Methods
AUTHORS:
Johnson Oladele Fatokun, Olabisi Akinwale, Shehu Abdulaziz
KEYWORDS:
Black-Scholes, Power Series Collocation, Adomian Decomposition, Financial Model, Partial Differential Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
24,
2025
ABSTRACT: In the contractual agreement of an option, the value at which the contract is settled is one of the pertinent factors to consider and the problem is to compute and come up with a model that encapsulates the current price of an asset, strike price of the option, asset’s volatility, maturity time and risk-free interest rate and the Black-Scholes model was the first model with all of these factors and this paper presents the algorithms to approximate solutions of Black Scholes financial model using the Adomian Decomposition and Power Series collocation methods, and presents comparative findings of the exact solution of Black Scholes financial model with approximate solutions from the Adomian Decomposition and Power Series collocation methods. The Adomian Decomposition method gives a better and more accurate result to the Power Series Collocation method for solving the Black Scholes financial model. Both methods are therefore efficient and agree with the exact solution of the model.