Intensity-Based Models (Reduced Form)
Unlike Structural Models (which watch the assets fall towards a barrier), Intensity-Based Models (or Reduced Form Models) treat default as a random "surprise" event. Major models: Jarrow-Turnbull (1995), Duffie-Singleton.
The Intensity (Lambda)
- We cannot see the firm's assets. We only see the "Hazard Rate" or "Default Intensity" ($\lambda$).
- Analogy: It's like a radioactive particle decay. We don't know mechanically why it decays, we just know the probability of it decaying in the next second.
How it works (Poisson Process)
Default is modeled as a Poisson Jump Process.
- Probability of Default in a short time $\Delta t$ is approx $\lambda \times \Delta t$.
- This $\lambda$ is calibrated from market prices (Bond Spreads or CDS spreads).
Inputs
Instead of assets and leverage, these models use Macroeconomic variables to drive intensity:
- Interest Rates
- GDP Growth
- Stock Market Return
- Unemployment
Why use them?
- Flexibility: Easier to calibrate to market prices of Corporate Bonds.
- Mathematically Tractable: Can handle complex derivatives (CDS valuation) better than Merton models.
Note
Structural vs Reduced Form:
- Structural: "Company defaulted because Assets < Liabilities." (Cause-based).
- Reduced Form: "Company defaulted because a random jump event occurred with intensity Lambda." (Statistical).
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