Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.

Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.

[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.