An Efficient Difference Algorithm for Black-Scholes Equation with Payment of Dividend

Abstract

Black-Scholes equation is the basic equation of option pricing in financial mathematics, it is important to study its numerical solution in financial market. This paper constructs a new kind of high order accuracy numerical algorithm (Three-layer difference scheme) for Black-Scholes equation with payment of dividend. Secondly, it gives the convergence of scheme. Thirdly, the stability and error estimates are analyzed. Finally, the numerical examples show the feasibility and effectiveness of the scheme. The truncation error of Three-layer scheme is little worse than CrankNicolson scheme and computational cost is little better than Crank-Nicoslon scheme. Therefore, the scheme is better suitable for applying to calculate the option pricing in the demanding high level of instantaneity. Keywords-component; Black-Scholes equation; Three-layer difference scheme; calculation stability; error estimate; numerical example