NUMERICAL SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS, USING EXPLICIT EULER-MARUYAMA METHODS

GANIYU A.A., FAMUAGUN K.S. and AKINREMI O.V.

Department of Mathematics,

Adeyemi College of Education, Ondo

ABSTRACT

This paper presented the solution of general first order stochastic differential equations (SDEs) using Explicit Euler-Maruyama (EEM) method. To implement the method, two SDEs of first order are solved. These are Black Scholes option price model (BSOPM) with a drift function and non-linear stochastic differential equations with multiplicative noise. The absolute errors are calculated using the exact solution and numerical solution for each value of independent variable in a given time interval. Comparison in the performance of the method was achieved using mean absolute error (MAE). The effect of varying stepsize of the method was examined. The accuracy of the method was also examined by determining the strong order of convergence of the method. The graphical solutions of the method applied to each problem were displayed for each of the stepsize.

Keywords: Stochastic Differential Equations (SDEs), Black Scholes Option Price Model with a Drift Function, Non-Linear SDEs with Multiplicative Noise, Explicit Euler-Maruyama Method, Exact Solution, Numerical Solution,  Mean Absolute error, Strong Order of Convergence.