Default and Asset Correlation

If default dependence is the heart of credit-risk modelling, then an empirical estimate of its magnitude is of primordial importance. Unlike estimation of default probabilities, addressed in the previous chapter, the characterization of default dependence is model dependent rendering this task more difficult. Since different models incorporate the relationship between obligor defaults in alternative ways, dependence is governed by some subset of a model’s parameters. As usual, a variety of techniques are presented, examined, and concretely implemented. The first, based on the method of moments, applies quite generally and is conceptually similar to the calibration techniques employed in previous chapters. A second approach, using observed default outcomes, exploits conditional independence to build a likelihood function and applies in both mixture and threshold settings. This permits use of the maximum-likelihood framework for the production of both point and interval estimates. The final, somewhat complex and fragile, approach is only applicable to the family of threshold models. It enjoys the advantage of using all transition data, but simultaneously requires inference of the unobservable global state variable values. The robustness of the final two techniques are assessed within separate simulation studies.