Convergence of Binomial Tree Method for European/American Path-Dependent Options

SIAM Journal on Numerical Analysis, Vol. 42, No. 3, pp. 1094-1109, 2004

20 Pages Posted: 21 Feb 2005

See all articles by Lishang Jiang

Lishang Jiang

Tongji University - Institute of Mathematics

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Abstract

The binomial tree method, first proposed by Cox et al. (1979), is the most popular approach to pricing options. By introducing an additional path-dependent variable, such method can be readily extended to the valuation of path-dependent options. Barraquand et al. (1996) presented the so-called forward shooting grid method, which is a modification of binomial tree method, to cope with arithmetic average options. In this paper, using numerical analysis and the notion of viscosity solutions, we present a unifying theoretical framework to show the uniform convergence of binomial tree methods for European/American path-dependent options, including arithmetic average options, geometric average options and lookback options.

Keywords: Binomial tree method, European/American path-dependent options, convergence

JEL Classification: 90A09, 91B28, 93E20

Suggested Citation

Jiang, Lishang and Dai, Min, Convergence of Binomial Tree Method for European/American Path-Dependent Options. SIAM Journal on Numerical Analysis, Vol. 42, No. 3, pp. 1094-1109, 2004. Available at SSRN: https://ssrn.com/abstract=669483

Lishang Jiang

Tongji University - Institute of Mathematics ( email )

1239 Siping Road
Shanghai, 200092
China

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

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