Hints for an extension of the early exercise premium formula for American options

TL;DR

This paper investigates the American put option pricing problem, highlighting the need for better mathematical understanding and proposing an extension to improve numerical methods and boundary approximations.

Contribution

It introduces an extension to the early exercise premium formula to address weaknesses in existing numerical approaches for American put options.

Findings

Identifies limitations in current numerical methods

Proposes an extension to the early exercise premium formula

Suggests improved boundary approximation techniques

Abstract

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.