An Improved Binomial Lattice Method for Multi-Dimensional Options

30 Pages Posted: 12 Sep 2005

See all articles by Andrea Gamba

Andrea Gamba

University of Warwick - Finance Group

Lenos Trigeorgis

University of Cyprus - Department of Public and Business Administration; King’s College London; Massachusetts Institute of Technology (MIT) - Sloan School of Management

Abstract

We propose a binomial lattice approach for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two main ideas: a transformation of the underlying processes as in the log-transformed binomial lattice approach by Trigeorgis (1991), and a change of basis of the asset span, to transform them into uncorrelated processes. These features improve the efficiency of the multi-dimensional binomial algorithm. We provide a thorough test of efficiency compared to most popular lattice approaches for multi-dimensional diffusions. Although the order of convergence is the same as in the other approaches the proposed approach shows improved efficiency.

Keywords: Option pricing, binomial lattice, multi-dimensional diffusion

JEL Classification: G13

Suggested Citation

Gamba, Andrea and Trigeorgis, Lenos, An Improved Binomial Lattice Method for Multi-Dimensional Options. Applied Mathematical Finance, Forthcoming, WBS Finance Group Research Paper No. 49, Available at SSRN: https://ssrn.com/abstract=798384

Andrea Gamba (Contact Author)

University of Warwick - Finance Group ( email )

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Lenos Trigeorgis

University of Cyprus - Department of Public and Business Administration ( email )

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King’s College London ( email )

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Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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