Randomized structural models of credit spreads

We propose to randomize the initial condition of a generalized structural model, where the solvency ratio instead of the asset value is modeled explicitly. This initial randomization assumption is motivated by the fact that market players cannot observe the solvency ratio accurately. We find that positive short spreads can be produced due to imperfect observation of the risk factor. The two models we have considered, the Randomized Merton (RM) and the Randomized Black--Cox (RBC) models, both have explicit expressions for the Probability of Default (PD) and Credit Spreads (CS). In the RM model, both PD and LGD are found to be of order , as the maturity T approaches zero. It therefore provides an example that has no well-defined default intensity but still admits positive short spreads. In the RBC model, the positive short spread is generated through the positive default intensity of the model. Because explicit formulas are available, these two Randomized Structure (RS) models are easily implemented and calibrated to market data. This is illustrated by a calibration exercise on Credit Default Swap (CDS) spread data of the Ford Motor Corporation.