Option pricing under Black-Scholes model using stochastic Runge-Kutta method.

Abstract: The purpose of this paper is solving the European option pricing problem under the Black–Scholes model. Our approach is to use the so-called stochastic Runge–Kutta (SRK) numericalscheme to find the corresponding expectation of the functional to the stochastic differentialequation under the Black–Scholes model. Several numerical solutions were made to study howquickly the result converges to the theoretical value. Then, we study the order of convergenceof the SRK method with the help of MATLAB.