Hints for an Extension of the Early Exercise Premium Formula for American Options

The 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 made to propose computational efficient methods but few of them have strong mathematical reasoning to ascertain why these methods work well and how important it is to consider a good approximation to the boundary or to the smooth pasting condition. We present an extension of the American put price aiming to catch weaknesses of the numerical methods given in the literature