A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model

Abstract

In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under the CEV model. In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables. The method is stable and has second-order convergence for both time and space variables. The convergence analysis of the proposed method is discussed in detail. Finally, numerical examples verify the stability and accuracy of the method.

Keywords

• CEV model
• barrier options
• cubic B-spline
• Crank-Nicolson method