Rare Disasters and Credit Market Puzzles

We embed systematic default, procyclic recovery rates and habit persistance into a model with a slight possibility of a macroeconomic disaster of reasonable magnitude. We derive analytical solutions for defaultable bond prices and show that a single set of structural parameters calibrated to the real economy and not to bond prices can simultaneously explain several key empirical regularities in credit markets. Our model captures the empirical level and volatility of credit spreads, generates a flexible credit risk term structure, and provides a good fit to a century of observed spreads. The model also matches the widespread skewness in index options. Finally, our model reveals a nonlinear relationship between bond and option prices that depends on the state of the economy and that helps explain conflicting empirical evidence found in the literature.