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.

An approximate method is developed for computing the values of European options on the maximum or the minimum of several assets. The method is very fast and is accurate for parameter ranges that are often of the most interest. The approach casts the problem in terms of order statistics and can be used to handle situations where the initial asset prices, the asset variances, and the covariances are all unequal. Numerical values are given to illustrate the accuracy of the method.

This paper examines the pricing of lookback and barrier options when the underlying asset follows the constant elasticity of variance (CEV) process. We construct a trinomial method to approximate the CEV process and use it to price lookback and barrier options. For look-back options, we find that the technique proposed by Babbs for the lognormal case can be modified to value lookbacks when the asset price follows the CEV process. We demonstrate the accuracy of our approach for different parameter values of the CEV process. We find that the prices of barrier and lookback options for the CEV process deviate significantly from those for the lognormal process. For standard options, the corresponding differences between the CEV and Black-Scholes models are relatively small. Our results show that it is much more important to have the correct model specification for options that depend on extrema than for standard options.