Financial
CDS Credit Triangle Hazard Rate & Cumulative Default Probability formulas
Estimate a constant risk-neutral hazard rate from a spread and assumed recovery, then calculate the corresponding model survival and default probabilities.
A simplified constant-intensity credit model
The credit-triangle approximation is spread=lambda*(1-recovery). Enter the annual spread as a decimal: 200 basis points is 0.02. Recovery 0.4 is an illustrative assumption, not a universal contractual rate. Lambda has units per year; T must use years.
The simplified relationship assumes constant hazard and recovery and abstracts from payment timing and other contract features. It is not a full CDS calibration: quotes can involve fixed coupons and upfront payments, and realistic pricing uses discounting and dated cash flows.
Under the assumed constant intensity, survival is exp(-lambda*T) and default probability is 1-survival. The market-implied quantity is risk-neutral, not a direct real-world forecast of bankruptcy; risk premia and other spread components matter. A zero input spread gives zero modeled hazard, not proof that an issuer is risk-free.
| CDS Credit Metric | Formula | 200 bps Spread, 40% Recovery, 5 Yr | Zero spread in this model |
|---|---|---|---|
| Loss Given Default (LGD) | 1 - B3 | 1 - 0.40 = 60.0% | 60.0% |
| Implied Hazard Rate lambda | B2 / (1 - B3) | 0.0200 / 0.60 = 3.33% / yr | 0.00% / yr |
| 5-Year Survival Prob Q(5) | EXP(-(B2 / (1 - B3)) * B4) | EXP(-0.1667) = 84.65% | 100.00% (1.0000) |
| 5-Year Cumulative Default PD | 1 - EXP(-lambda * T) | 15.35% (0.1535) | 0.00% (0.0000) |
Cumulative T-Year Market-Implied Default Probability PD(T)
For finite nonnegative intensity and horizon, the mathematical probability lies between zero and one. Four-decimal rounding, or floating-point underflow in extreme inputs, can display exactly 1; do not claim it is always displayed strictly below 100%.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<0,B3>=1,B4<0),"Invalid inputs",ROUND(1 - EXP(-(B2 / (1 - B3)) * B4), 4)))Constant annual hazard rate
Recovery must be at least zero and below one. A negative spread is outside this simple model. Hazard is an intensity, not a one-year probability; convert it with the exponential model.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<0,B3<0,B3>=1),"Invalid inputs",ROUND(B2 / (1 - B3), 4)))Survival under the same constant intensity
Calculate from the unrounded spread and recovery inputs, rather than the displayed rounded hazard. Survival and default probabilities complement one another within the model.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<0,B3<0,B3>=1,B4<0),"Invalid inputs",ROUND(EXP(-(B2 / (1 - B3)) * B4), 4)))Try the example
Use the original values or change them to test your understanding.