Prices of State-Contingent Claims Implicit in Option Prices

Abstract

The time-state preference approach to general equilibrium in an economy as developed by Arrow (1964) and Debreu (1959) is one of the most general frameworks available for the theory of finance under uncertainty. Given the prices of primitive securities (a security that pays $1.00 contingent upon a given state of the world at a given date, and zero otherwise, is a primitive This paper implements the time-state preference model in a multiperiod economy, deriving the prices of primitive securities from the prices of call options on aggregate consumption. These prices permit an equilibrium valuation of assets with uncertain payoffs at many future dates. Furthermore, for any given portfolio, the price of a $1.00 claim received at a future date, if the portfolio's value is between two given levels at that time, is derived explicitly from a second partial derivative of its calloption pricing function. An intertemporal capital asset pricing model is derived for payoffs that are jointly lognormally distributed with aggregate consumption. It is shown that using the Black-Scholes equation for options on aggregate consumption implies that individuals' preferences aggregate to isoelastic utility.