Crank Nicolson Approach for the Valuation of the Barrier Options

Abstract

Barrier options are considered to be cheaper than the standard options as they provide lower premiums which make them to be attractive to hedgers in the financial market. In this article, the numerical procedure for the valuation of the barrier option is presented under the Black-Scholes framework. This procedure incorporates the explicit together with implicit finite difference approach. To obtain an accurate price of the considered barrier options, a grid is constructed such that we have the barrier located in a suitable position. The numerical result obtained is being compared with the exact value of the option and it shows that this approach converges faster to the exact value with smaller time step.