On the Consistency of the Black-Scholes Model with a General Equilibrium Framework

Abstract

We construct a simple economy with consumption only at the final date in which we “endogenize” the stochastic behavior of prices assumed in the Black-Scholes model. Certain preferences (constant proportional risk aversion) and beliefs are shown to be sufficient and necessary, in certain respects, for the existence of such an equilibrium. The analysis is then generalized to a continuous-consumption framework, in which we embed the Merton proportional dividend model.