B-splines Method with Redefined Basis Functions for Solving Barrier Options Pricing Model

In this paper, we construct a numerical method to the solution of Black-Scholes partial differential equation modelling Barrier option pricing problem on a single asset. We use finite difference approximations for temporal derivative and then the option price is approximated with the redefined B-spline functions. Stability of this method has been discussed and shown that it is unconditionally stable. The developed method is tested on down-and-out Barrier problem and the numerical results are reported in tabular form where approximation solutions are compared with exact ones. They show the numerical results are in good agreement with exact solutions.