We develop a numerical approximation method for valuing multivariate contingent claims. The approach is based on an n-dimensional extension of the lattice binomial method. Closed-form solutions for the jump probabilities and the jump amplitudes are obtained. The accuracy of the method is illustrated in the case of European options when there are three underlying assets.

In 1987, Lo derived an upper bound on the price of a European call option on a single asset. Lo's bound depends only on the mean and variance of the terminal asset price and is termed a semi-parametric bound. This paper derives similar semi-parametric bounds on a European call on the maximum of any number of assets. A distribution-free bound for the price of this option is obtained. The bound depends only on the means and covariance matrix of the returns on n underlying assets. The bound is obtained by optimizing over the entries of a positive definite matrix A. This can be accomplished by a technique known as semidefinite programming. We demonstrate the methodology using two specific applications. The first concerns the valuation of a European call option on the maximum of several assets. This is known as an outperformance option and is of some practical interest. The second application concerns the valuation of a discretely adjusted lookback option. These lookback options are of interest in connection with certain equity annuity insurance products.

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.