Numerical option pricing without oscillations using flux limiters

A numerical method is developed for the solution of the Black–Scholes equation avoiding the oscillations that are common close to a discontinuity in the pay-off function. Part of the derivatives are evaluated explicitly and part of them are computed implicitly using operator splitting. The method is second order accurate in time and almost of second order in the asset price for smooth solutions and no system of nonlinear equations has to be solved. A flux limiter modifies the first derivative in the equation such that no oscillations occur in the solution in the numerical examples presented.