Rare Disasters, Credit, and Option Market Puzzles

We embed systematic default, procyclical recovery rates, and external habit persistence 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 can simultaneously explain several key empirical regularities in equity, credit, and options 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 high-yield and collaterized debt obligation tranche spreads, equity market moments, and index option skewness. Finally, our model implies a time-varying relationship between bond and option prices that depends on the state of the economy and that explains the conflicting empirical evidence found in the literature.