  Characterization of the American put option price is still an open issue.
  From the beginning of the nineties there exists a non-closed formula for this
price but nontrivial numerical computations are required to solve it. Strong
efforts have been done to propose methods more and more computationally
efficient but most of them have few mathematical ground as to ascertain why
these methods work well and how important is to consider a good approximation
to the boundary or to the smooth pasting condition. We perform an extension of
the American put price aiming to catch weaknesses of the numerical methods
given in the literature.
