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

Authors

  • Daniel Sevcovic
  • M. Lauko

DOI:

https://doi.org/10.21914/anziamj.v51i0.2923

Keywords:

option pricing, American put option, early exercise boundary, limiting behaviour close to expiry

Abstract

We present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our 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 [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance 9 (2006) 1141–1177]. doi:10.1017/S1446181110000854

Published

2011-05-03

Issue

Section

Articles for Printed Issues