Euler-Maruyama Approximation of Stochastic Dependent Poisson-Jump in Black-Scholes Asset Price Model

Abstract

In this study, the Gaussian white noise and the differential Poisson of the Stochastic Differential Equation(SDE) with distributed jump are examined. Using Ito integral as a tool, a one step Euler-Maruyama (E-M) method is considered for the approximation of Stochastic Dependent Poisson Analysis (SDPA) in finance. The Deterministic Quadrature Rule (DQR) was used in the establishment of the method for easy examination of the Black-Scholes asset price model for stock investors; MATLAB package was used for simulation of the method. However the Mean Absolute Error (MAE) as well as Strong Order of Convergence (SOC) method was considered to ascertain its usability. The result clearly shows entry points and exit points of stock market. Consequently, the findings of this research is strongly recommended. Keywords: Euler-Maruyama method, Stochastic differential equation, Ito integral, Poisson distributed jump, Random variables, Deterministic model.