Spanning and derivative-security valuation

This article provides the economic foundations for valuing derivative securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. From the characteristic function of the state-price density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. The strength and versatility of the methodology is inherent when valuing (1) average-interest options, (2) correlation options, and (3) discretely monitored knock-out options. (C) 2000 Elsevier Science S.A, All rights reserved. JEL classification: CIO; G12; G13.