Achieving Smooth Asymptotics for the Prices of European Options in Binomial Trees

15 Pages Posted: 5 Sep 2006 Last revised: 14 Feb 2008

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Date Written: September 2006

Abstract

A new binomial approximation to the Black-Scholes model is introduced. It is shown that for digital options and vanilla European call and put options that a complete asymptotic expansion of the error in powers of 1/n exists. This is the first binomial tree for which such an asymptotic expansion has been shown to exist.

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

JEL Classification: G13

Suggested Citation

Joshi, Mark S., Achieving Smooth Asymptotics for the Prices of European Options in Binomial Trees (September 2006). Available at SSRN: https://ssrn.com/abstract=928186 or http://dx.doi.org/10.2139/ssrn.928186

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

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