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Default, Recovery, and Hazard Rate

One-line definition

Modeling credit loss as a probability of default times the loss given default, using a constant hazard rate as the simplifying assumption.

Formulas

Survival to time t: S(t) = exp(-hazard_rate * t)

Expected loss: EL = Notional * PD * (1 - RecoveryRate)

Implied par spread: spread ≈ hazard_rate * (1 - RecoveryRate)

Why PMs care

This is the building block behind both CDS pricing and risky-bond valuation — a credit spread is compensation for exactly this expected loss (plus a risk premium above the pure actuarial expectation).

Common mistakes

  • treating recovery rate as constant across the cycle — recoveries fall in systemic downturns, exactly when defaults rise
  • confusing a constant hazard rate (memoryless) with a real issuer's actual default-timing profile, which usually isn't constant

Limitations

Constant hazard rate is a simplification. Real credit curves imply a term structure of hazard rates, and real spreads include a risk premium above the pure expected-loss compensation shown here.