qt = (Ct − Ct−1) ÷ (1 − Ct−1). This conditions the next-year default probability on survival to the start of the year.
Illustrative data only. Replace every sample curve and transition assumption before CECL or IFRS 9 use.
From cumulative curve to decision-ready PD
Edit assumptions, compare TTC and PIT outcomes, then export a review-ready term structure.
12-month PD · TTC0.280%
12-month PD · PIT0.235%+0.045%
Lifetime PD · TTC3.04%
Lifetime PD · PIT2.10%5y horizon
Cumulative probability of default
Source: Markov migration curveMigration: AppliedPIT: Vasicek active
Editable term structure ledger
| Year | TTC cumulative | TTC 12m | PIT cumulative | PIT 12m | Source |
|---|---|---|---|---|---|
| 1 | 0.280% | 0.280% | 0.235% | 0.235% | Migration |
| 2 | 0.726% | 0.447% | 0.620% | 0.386% | Migration |
| 3 | 1.34% | 0.618% | 1.16% | 0.545% | Migration |
| 4 | 2.11% | 0.785% | 1.63% | 0.474% | Migration |
| 5 | 3.04% | 0.943% | 2.10% | 0.476% | Migration |
| 6 | 4.09% | 1.09% | 2.65% | 0.565% | Migration |
Methodology and assumptions
Every displayed result is traceable from the selected TTC source through migration, PIT conditioning, and ECL.
Φ[(Φ⁻¹(qTTC) − √ρZ) ÷ √(1−ρ)]. Scenario PIT values are blended using editable probability weights.
Each scenario’s Z factor applies for three years, then decays linearly to zero over two years. Thereafter PIT equals TTC.
A one-year Markov transition matrix propagates rating-state probabilities. Default is absorbing; the cumulative default-state probability becomes the TTC curve.
PD over the remaining maturity is conditional on survival through seasoning: (Cend − Cstart) ÷ (1 − Cstart).
Discounted ECL = PD × LGD × EAD ÷ (1 + effective interest rate)maturity. This calculator uses a single lifetime exposure approximation.
Important limitations. Sample curves and transition probabilities are illustrative. Migration is applied to the TTC layer; the matrix is not separately stressed by scenario. API ingest/push from the earlier prototype is intentionally omitted from this public browser app because secured endpoints require a backend proxy and credentials must not be exposed client-side.