A Fast Numerical Method for a Nonlinear Black-Scholes Equation

摘要

In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s,t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed.