This paper examines some implications of using an estimate of the variance in option valuation models. This procedure produces biased option values. It is shown that the magnitude of this bias is not large. The dispersion induced in the option price is more significant particularly for parameter values of practical interest. The nature and extent of this dispersion is examined by numerical examples. The paper suggests how a Bayesian approach could be used to cope with the estimation error.

[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.]

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.

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.