Correlation in corporate defaults: Contagion or conditional independence?

We revisit a method used by Das et al. (2007) (DDKS) who jointly test and reject a specification of firm default intensities and the doubly stochastic assumption in intensity models of default. The method relies on a time change result for counting processes. With an almost identical set of default histories recorded by Moody’s in the period from 1982 to 2006, but using a different specification of the default intensity, we cannot reject the tests based on time change used in DDKS. We then note that the method proposed by DDKS is mainly a misspecification test in that it has very limited power in detecting violations of the doubly stochastic assumption. For example, it will not detect contagion which spreads through the explanatory variables “covariates” that determine the default intensities of individual firms. Therefore, we perform a different test using a Hawkes process alternative to see if firm-specific variables are affected by occurrences of defaults, but find no evidence of default contagion.     

Decomposing swap spreads

We analyze a six-factor model for Treasury bonds, corporate bonds, and swap rates and decompose swap spreads into three components: a convenience yield from holding Treasuries, a credit risk element from the underlying LIBOR rate, and a factor specific to the swap market. The convenience yield is by far the largest component of spreads. There is a discernible contribution from credit risk as well as from a swap-specific factor with higher variability which in certain periods is related to hedging activity in the mortgage-backed security market. The model also sheds light on the relation between AA hazard rates and the spread between LIBOR rates and General Collateral repo rates and on the level of the riskless rate compared to swap and Treasury rates.     

On cox processes and credit risky securities

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.