Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral.First, our Binomial No-Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no default.Thus actual default is irrelevant, though the potential for default drives the equilibrium and limits borrowing.This result is valid with arbitrary preferences and endowments, arbitrary promises, many assets and consumption goods, production, and multiple periods.We also show that the no-default equilibrium would be selected if there were the slightest cost of using collateral or handling default.Second, our Binomial Leverage Theorem shows that equilibrium LT V for non-contingent debt contracts is the ratio of the worst-case return of the asset to the riskless rate of interest.Finally, our Binomial Leverage-Volatility theorem provides a precise link between leverage and volatility.

We provide a pricing theory for emerging asset classes, like emerging markets, that are not yet mature enough to be attractive to the general public. We show how leverage cycles can cause contagion, flight to collateral, and issuance rationing in a frequently recurring phase we call the anxious economy. Our model provides an explanation for the volatile access of emerging economies to international financial markets, and for three stylized facts we identify in emerging markets and high yield data since the late 1990s. Our analytical framework is a general equilibrium model with heterogeneous agents, incomplete markets, and endogenous collateral, plus an extension encompassing adverse selection.

Savings and Portfolio Choice in a Two-Period Two-Asset Model by Saku Aura, Peter Diamond and John Geanakoplos. Published in volume 92, issue 4, pages 1185-1191 of American Economic Review, September 2002

We provide a theorem giving a set of conditions under which public observation of an aggregate of individual expectations leads to consensus. The key concept unkerlying the result is that of common knowledge, as formalized by Aumann (1976)

A firm’s actions in one market can change competitors’ strategies in a second market by affecting its own marginal costs in that other mar-ket. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market and (b) whether competitors’ products are strategic substitutes or strategic complements. The latter distinction is determined by whether more “aggressive” play (e.g., lower price or higher quantity) by one firm in a market lowers or raises compet-ing firms’ marginal profitabilities in that market. Many recent results in oligopoly theory can be most easily understood in terms of strategic substitutes and complements.

Systemic risk must include the housing market, though economists have not generally focused on it. We begin construction of an agent-based model of the housing market with individual data from Washington, DC. Twenty years of success with agent-based models of mortgage prepayments give us hope that such a model could be useful. Preliminary analysis suggests that the housing boom and bust of 1997-2007 was due in large part to changes in leverage rather than interest rates.