Comparison of numerical and analytical approximations of the early exercise boundary of the American put option

TL;DR

This paper compares analytical and numerical methods for approximating the early exercise boundary of American put options, introduces a new numerical scheme, and evaluates its accuracy against existing methods.

Contribution

It introduces a novel numerical scheme based on a nonlinear integral equation for computing the early exercise boundary of American put options.

Findings

The new numerical method provides accurate boundary approximations.

Comparison shows the new scheme outperforms existing methods in certain regimes.

Analytical approximations are validated near expiration.

Abstract

In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the paper, we introduce a new numerical scheme for computing the entire early exercise boundary. The local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over relaxation method and the analytical approximation formula recently derived by Zhu.