Pricing credit risk and default potential have always been important research topics and the credit crisis of 2007 and 2008 has generated even greater interest. Numerous empirical studies of credit spreads have been performed. For example, Krishnan, Ritchken and Thomson (2006) use credit spread slopes of bank debt to predict bank risk. As others, they find the shape of the credit spread can be positive or negative and is often humped. Furthermore, they find that over time the credit spread can change in different ways for individual banks.
Our purpose is to analyze the shape of credit spread term structures. More specifically, we analyze the term structure of first passage default and, in turn, its impact upon term structures of default risky yields and credit spreads. We analyze how these term structures depend on such things as covenants, the volatility of interest rates, volatility of firm value, correlation of firm value with interest rates, and other model parameters. A hump in first passage default can encourage a hump in credit spread but is not necessary for a hump to occur. Conditions for a hump in term structures are particularly interesting and useful to explain. Furthermore, the impact of (weak) covenants upon these term structures is particularly timely given the recent credit crisis.
As we show, it is important to separate default due to breach of barrier versus default due to assets being less than face value at maturity. Certain industries and firms may have a hump in term structure of default probability due to strength of covenants (barriers) where others do not. To our knowledge, we are the first to apply and analyze Giesecke's (2004) separation of default probabilities. Of course, banking regulators should find anything which helps predict default risk and the health of the banking system very useful in developing regulation policies.
Even though credit spread models have been found very useful, a number of empirical studies have noted a lack of explanatory power. Collin-Dufresne, Goldstein and Martin (2001) find that some variables that should explain credit spread changes have only limited explanatory power. In an effort to increase explanatory power, Driessen (2005), for example, focuses on adding an event risk premium but finds such a premium cannot be estimated very well. Christensen (2008) refers to the inability of empirical models to explain credit spreads as the 'corporate bond credit spread puzzle'. The limitations of these empirical findings using extant models suggest a need for improved theoretical models that utilize firm specific or industry specific factors such as covenants and default barriers and, also, a need to segregate default probability into that due to barrier (covenants) versus classic Merton (1974) maturity default.
