The Convexity of the Free Boundary for the American put option

TL;DR

This paper investigates the convexity of the early exercise boundary in American put options, providing a condition under which this boundary is convex, based on a free boundary problem in option pricing.

Contribution

It introduces a new condition ensuring the convexity of the early exercise boundary in American put options, advancing understanding of free boundary problems in finance.

Findings

Established a convexity condition for the free boundary.

Provided theoretical insights into the shape of the early exercise boundary.

Enhanced mathematical understanding of American option valuation.

Abstract

This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a geometric Brownian motion process. The contribution is to propose a condition for that the early exercise boundary is a convex function.