Default and Systemic Risk in Equilibrium

by Agostino Capponi of Purdue University, and
Martin Larsson of Cornell University

December 23, 2011

Abstract: We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process, and a defaultable bond, whose prices are determined via equilibrium. We analyze the endogenous interaction arising between the stock and the defaultable bond via the interplay between equilibrium behavior of investors, risk preferences and cyclicality properties of the default intensity. We find that the equilibrium price of the stock experiences a jump at default, despite that the default event has no causal impact on the dividend process. We characterize the direction of the jump in terms of a relation between investor preferences and the cyclicality properties of the default intensity. We conduct a similar analysis for the market price of risk and for the investor wealth process, and determine how heterogeneity of preferences affects the exposure to default carried by different investors.

JEL Classification: G12, G11, P34, E44.

AMS Classification: 60E15, 60H30.

Keywords: contagion, default risk, equilibrium, systemic risk, stochastic orderings.

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