In the option-based models studied so far, the default event is defined in terms of the process modeling the assets of an issuer. Default is triggered when assets, or some function thereof, hit (or fall below) some boundary. We now move to a different class of models, the intensity models, which model factors influencing the default event but typically (but not necessarily) leave aside the question of what exactly triggers the default event.
There are two main reasons why intensity models are important in the study of default risk. First, intensity models clearly seem to be the most elegant way of bridging the gap between credit scoring or default prediction models and the models for pricing default risk. If we want to incorporate into our pricing models not only the firm’s asset value but other relevant predictors of default, we could turn to the default prediction models and ask which covariates are relevant for predicting default. To turn this into a pricing model we need to understand the dynamic evolution of the covariates and how they influence default probabilities. The natural framework for doing this is the intensity-based models which link hazard regressions with standard pricing machinery.
Second, the mathematical machinery of intensity models brings into play the entire machinery of default-free term-structure modeling. This means that econometric specifications from term-structure modeling and tricks for pricing derivatives can be transferred to defaultable claims. Furthermore, some claims, such as basket default swaps, whose equivalent is not readily found in ordinary term-structure modeling, also turn out to be conveniently handled in this setting.
In ordinary term-structure modeling, our ignorance of what truly governs the dynamics of interest rates is often hidden in an “exogenous” specification of (say) the short rate. This use of exogenous specifications will be transferred into the default-risk setting, where most models use exogenously given specifications of the intensity of default. The mathematical structure for ordinary term-structure modeling easily allows, however, for the short rate to depend on multidimensional state variable processes and even to depend on observable state variable processes. It is mainly the trouble of specifying good models for this dependence which forces us