Spanning and Derivative-Security Valuation
Journal of Financial Economics, Vol. 55, Iss. 2
Posted: 20 May 1999
There are 2 versions of this paper
Abstract
This paper shows that a continuum of options and a continuum of characteristic functions are equivalent classes of spanning securities, for a wide class of payoff functions. 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. In one specific application, 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. Possible extensions to our work include the pricing of American options from the characteristic function, and the recovery of the risk-neutral density from the continuum of out-of-money calls and puts. We provide the economic foundations for valuing derivative securities.
Note: This is a description of the paper and not the actual abstract.
JEL Classification: G10, G12, G13
Suggested Citation: Suggested Citation