Quantity-Adjusting Options and Forward Contracts

Quantity-adjusting option and forward contracts deliver a payoff on a variable quantity of underlying. This article explains the use, pricing, and hedging of such contracts. The pricing of product options is also derived. Product options include quantity-adjusting options as a special case and pay off as a function of the prices of four risky assets. The pricing formula for these options is reduced to an expression in a two-dimensional density from a four-dimensional one. Closed form solutions in terms of the bivariate normal are obtained. Similar formulae in terms of the univariate normal are obtained for quantity-adjusting options. The normal distribution is absent from the expression for quantity-adjusting forwards. Product options also include sequential switching, or guru options. These are options which guarantee optimal asset selection at present dates among a fixed set of traded assets