We show that binomial economies with ﬁnancial assets are an informative and tractable model to study endogenous leverage and collateral equilibrium: endogenous leverage can be highly volatile, but it is always easy to compute. The possibility of default can have a dramatic eﬀect on equilibrium, if collateral is scarce, yet we prove the No-Default Theorem asserting that, without loss of generality, there is no default in equilibrium. Thus potential default has a dramatic eﬀect on equilibrium, but actual default does not. This result is valid with arbitrary preferences, contingent promises, many assets and consumption goods, production, and multiple periods. On the other hand, we show that the theorem fails in trinomial models. For example, in a CAPM model, we ﬁnd that default is robust. In a model with heterogeneous beliefs, we ﬁnd that diﬀerent agents might borrow on the same asset with diﬀerent LTVs .
Fostel, Ana and Geanakoplos, John, "Endogenous Leverage in a Binomial Economy: The Irrelevance of Actual Default" (2012). Cowles Foundation Discussion Papers. 2242.