High order approximation of derivatives with applications to pricing of financial derivatives

Abstract In this paper, we first compare three different methods for approximating the first and second derivatives from function values given at scattered points. Then we propose to use the most accurate derivative approximation method in a forward Euler scheme to solve the general Black–Scholes equation. We prove the scheme’s stability and error estimate. Many numerical examples applying to pricing of financial derivatives are presented to demonstrate the efficiency and accuracy of our scheme.