Download this Paper Open PDF in Browser

Achieving Higher Order Convergence for the Prices of European Options in Binomial Trees

14 Pages Posted: 3 Apr 2007 Last revised: 14 Feb 2008

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Multiple version iconThere are 2 versions of this paper

Date Written: October 8, 2007

Abstract

A new family of binomial trees as approximations to the Black-Scholes model is introduced. For this class of trees, the existence of complete asymptotic expansions for the prices of vanilla European options is demonstrated and the first three terms are explicitly computed. As special cases, a tree with third order convergence is constructed and the conjecture of Leisen and Reimer that their tree has second order convergence is proven.

Keywords: binomial trees, Richardson extrapolation, options, rate of convergence

JEL Classification: G13

Suggested Citation

Joshi, Mark S., Achieving Higher Order Convergence for the Prices of European Options in Binomial Trees (October 8, 2007). Available at SSRN: https://ssrn.com/abstract=976561 or http://dx.doi.org/10.2139/ssrn.976561

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Paper statistics

Downloads
1,044
Rank
16,250
Abstract Views
3,176