Browsing by Author "Nwachukwu, O. O"

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    NUMERICAL APPROXIMATION OF BLACK SCHOLES STOCHASTIC DIFFERENTIAL EQUATION USING EULER-MARUYAMA AND MILSTEIN METHODS
    (university of el oued/جامعة الوادي, 2021-01-01) Nwachukwu, O. O
    This 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.