Perpetual American Put Option: An Error Estimator For A Second Order Non-Standard Finite Di¤erence Scheme

In this paper, we present the numerical result obtained by a MATLAB version of a second order non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. These models can be derived from the celebrated Black-Scholes models letting the time go to infinity. The considered problem is a free boundary problem defined on a semi infinite interval so that it is a non-linear problem complicated by a boundary condition at infinity. By using non-uniform maps and non-standard finite differe scheme, we show how it is possible to apply the boundary condition at infinity exactly. Moreover, we define a posteriori error estimator that is based on the Richardson classical extrapolation theory. nite di¤erence scheme and error estimator are favourably tested for a simple problem with a known exact analytical solution, the scheme is found to be of second order accuracy.