  For the numerical solution of the American option valuation problem, we
provide a script written in MATLAB implementing an explicit finite difference
scheme. Our main contribute is the definition of a posteriori error estimator
for the American options pricing which is based on Richardson's extrapolation
theory. This error estimator allows us to find a suitable grid where the
computed solution, both the option price field variable and the free boundary
position, verify a prefixed error tolerance.
