Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model  

作　　者：Henrietta Ify Ojarikre Ideh Rapheal Ebimene James Mamadu Henrietta Ify Ojarikre;Ideh Rapheal;Ebimene James Mamadu(Department of Mathematics, Delta State University, Abraka, Nigeria)

机构地区：[1]Department of Mathematics, Delta State University, Abraka, Nigeria

出　　处：《Journal of Applied Mathematics and Physics》2024年第3期819-828,共10页应用数学与应用物理（英文）

摘　　要：Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

关 键 词：Elzaki Transform Method European Call Black-Scholes Model Fokker-Planck Equation Market Volatility 

分 类 号：O17[理学—数学]