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A Lattice Framework for Option Pricing with Two State Variables

Published online by Cambridge University Press:  06 April 2009

Phelim P. Boyle
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Abstract

A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to price any contingent claim whose payoff is a piece-wise linear function of two underlying state variables, provided these two variables have a bivariate lognormal distribution. The accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for European options. One advantage of the lattice approach is that it handles the early exercise feature of American options. In addition, it should be possible to use this approach to value a number of financial instruments that have been created in recent years.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 23 , Issue 1 , March 1988 , pp. 1 - 12
Copyright
Copyright © School of Business Administration, University of Washington 1988

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