Solution of the Black-Scholes equation for pricing of barrier option

Abstract

In this paper two different methods are presented to approximate the solution of the Black-Scholes equation for valuation of barrier option. These techniques can be applied directly for all types of differential equations, homogeneous or inhomogeneous. The use of these methods provides the solution of the problem in a closed form while the mesh point techniques provide the approximation at mesh points only. Also, the two schemes need less computational work in comparison with the traditional methods. These techniques can be employed for problems with initial condition. In this paper we use the variational iteration and homotopy perturbation methods for solving the Black-Scholes equation with terminal condition. Numerical results are compared with theoretical solutions in order to confirm the validity of the presented procedures. © 2011 Verlag der Zeitschrift für Naturforschung, Tübingen.