Financial Innovation and Endogenous Uncertainty in Incomplete Asset Markets

We study endogenous uncertainty stemming from the introduction of new financial assets, so as to evaluate the risks as well as the welfare gains of financial innovation. The introduction of financial assets to hedge individual risk can lead to the risk of default, which is a collective risk. The possibility of default represents endogenous uncertainty, since it depends on economic variables. A proper allocation of risk in the face of new states of endogenous uncertainty requires the introduction of a large number of additional new securities, without which the market is incomplete. We prove the existence of a general equilibrium with default, in which the agents recontract trading positions and prices in the states of default (Theorem 1). We establish the existence of an open set of general equilibrium economies, called complex economies, in which the pattern of trade is highly interconnected so that default by one agent leads to default by overwhelming majority of all other individuals (Theorem 2). We exhibit examples of complex economies in which the expected amount of default increases with the population (Proposition 3, Examples 3, and 4).