Nwachukwu, O. O2023-05-292023-05-292021-01-01O. O. Nwachukwu,NUMERICAL APPROXIMATION OF BLACK SCHOLES STOCHASTIC DIFFERENTIAL EQUATION USING EULER-MARUYAMA AND MILSTEIN METHODS .Journal of Fundamental and Applied Sciences.VOL13 N01.01/01/2021.university of el oued [visited in ../../….]. available from [copy the link here]1112 9867http://dspace.univ-eloued.dz/handle/123456789/24647ARTICLEThis paper will introduce the Ito’s lemma used in the stochastic calculus to obtain the Ito-Taylor expansion of a stochastic differential equations. The Euler-Maruyama and Milstein’s methods of solving stochastic differential equations will be discussed and derived. We will apply these two numerical methods to the Black-Scholes model to obtain the values of a European call option of a stock at discretized time intervals. We will use a computer simulation to approximate while using the Ito’s formula to obtain the exact solution. The numerical approximations to the exact solution to infer on the effectiveness of the two methods.enStochastic differential equations; Euler-Maruyama method; Milstein method; Black-Scholes equation; Call option.Article