Credit Intensity Models and Default Correlation
Intensity models treat default as a random time with a hazard rate, which can be linked across names via factors.
In reduced-form models, default time is generated from an intensity (hazard rate) process, not a structural threshold.
Common factors in intensities generate dependent default times and cluster risk in portfolios.
Default correlation matters for CDO tranches, tail risk, and systemic stress testing.
Intensity models treat default as a random time driven by a hazard rate. When a common factor drives part of that intensity, different names share stress periods and default times become clustered rather than independent.
Increasing ρ moves more of λ into the common factor: the purple segments grow relative to the grey ones, especially in the stress scenario. Single-name default probabilities change only moderately, but the joint default and “at least one default” bars grow faster.
The correlation number summarises clustering: with ρ near zero, defaults are almost independent; with large ρ, stress periods dominate and defaults become much more likely to occur together. This is exactly the effect that matters for portfolio credit, tranches, and systemic stress testing.