Existence of competitive equilibria for option markets

In a general equilibrium model with options, H. Polemarchakis and Bon-Il Ku ("Options and Equilibrium," Working Paper, Columbia University 1986) give an example of an economy where no competitive equilibrium exists. Their model is robust in the sense that slight changes of the parameters of the economy do not lead to the existence of an equilibrium. The aim of this paper is to show that this nonexistence of equilibrium results from too little variation of the aggregate supply of commodities over the states of the world. We show that the fraction of economies (parameterized by endowments) with equilibria converges to one with increasing variation in the total endowment, in a precise sense.