Incorporating Risk Aversion and Model Misspecification into a Hybrid Model of Default

Abstract:     
It is well known that purely structural models of default cannot explain short term credit spreads, while purely intensity based models of default lead to completely unpredictable default events. Here we introduce a hybrid model of default in which a firm enters distress upon a non-tradable credit worthiness index (CWI) hitting a critical level. Upon distress, the firm defaults at the next arrival of a Poisson process. To value defaultable bonds and CDSs we introduce the concept of robust indifference pricing which differs from the usual indifference valuation paradigm by the inclusion of model uncertainty. To account for model uncertainty, the embedded optimization problems are modified to include a minimization over a set of candidate measures equivalent to the estimated reference measure. With this new model and pricing paradigm, we succeed in determining corporate bond spreads and CDS spreads and find that model uncertainty plays a similar, but distinct, role to risk aversion. In particular, model uncertainty allows for significant short term spreads.

Keywords: Strucutural Models, Intensity Models, Stochastic Optimal Control, Robust Optimization, Indifference Valuation, Defaultable Bonds, Credit Default Swap

Working Paper Series