Spline approximation method to solve an option pricing problem

Abstract

In this paper we construct a numerical method based on spline approximations to solve a nonlinear Black–Scholes partial differential equation modelling European option pricing problem on a single asset. We use the classical Euler implicit method for the time discretization and a B-spline collocation method for the spatial discretization. The method is shown to be unconditionally stable and accurate of order . The computational performance of the proposed scheme is compared via numerical results obtained using a scheme based on the quasi-radial basis functions.

Keywords:

• option pricing
• Black–Scholes equation
• B-spline collocation
• convergence analysis

2000 Mathematics Subject Classification::

• 39A05
• 65M06
• 65M12

Acknowledgements

The authors thank the referees for their valuable suggestions. MHMK acknowledges the financial support from the Sudan University of Science and Technology (SUST), Sudan. KCP was also supported by the South African National Research Foundation.