Example data table
| Scenario | Method | Key inputs | Output (PD) |
|---|---|---|---|
| Retail portfolio snapshot | Historical | Total=1000, Defaults=25, Window=1y | 2.5000% annualized |
| Bond spread estimate | Hazard | Spread=180bps, Recovery=0.40, Tenor=5y | ≈ 13.9346% over 5y |
| Firm balance sheet | Structural | V=50m, D=35m, σ=0.35, r=0.05, T=1y | Model-derived |
| Scorecard output | Logistic | a=-3.2, b=0.004, x=650 | Model-derived |
Illustrative only; calibrate inputs and assumptions for your context.
Formula used
Historical default rate: Window rate = Defaults / Total. Annualized PD = 1 − (1 − Window rate)1/WindowYears.
Hazard approximation: λ ≈ Spread / (1 − Recovery). PD(T) = 1 − e−λT.
Structural (Merton, simplified): d2 = [ln(V/D) + (r − 0.5σ²)T] / (σ√T). PD = N(−d2).
Logistic model: z = a + b·x. PD = 1 / (1 + e−z).
Use calibrated parameters and consistent horizons for analysis.
How to use this calculator
- Select a method that matches your available data.
- Enter values; use decimals for rates and volatility.
- Press calculate to display PD and model details.
- Export CSV or PDF for documentation and review.
Portfolio-level PD monitoring
Banks summarize default risk with one-year PDs, then translate them into multi-year views for capital planning. An annual PD of 2.5% implies a five-year cumulative PD near 11.8% under a constant-hazard approximation, which can change credit loss timing and buffers. Analysts track PD by segment, then relate movements to macro drivers such as unemployment and policy rates.
Historical rate signals
With 25 defaults across 1,000 exposures, the window default rate equals 2.5%. If the observation window is three years, annualizing avoids overstating risk; a 7.2% three-year rate corresponds to about 2.46% per year assuming independent default events. For smaller samples, add uncertainty: with 25 defaults, a rough binomial standard error is about 0.49%, so quarterly PDs can move noisily.
Market-implied spread interpretation
Credit spreads embed compensation for expected default, liquidity, and risk premia. With a 180 bps spread and 40% recovery, the hazard estimate gives λ ≈ 0.03, producing a one-year PD around 2.96% and a five-year PD near 13.9%. If recovery falls to 25% with the same spread, λ increases and the cumulative PD rises, tightening pricing headroom.
Structural distance-to-default view
Structural models link PD to asset value, leverage, and volatility. A higher V/D ratio reduces PD, while higher σ increases it. Even with identical leverage, raising σ from 25% to 40% can lift PD because downside dispersion grows with time. Risk teams run sensitivities, shifting V by ±10% and σ by ±5%, to see how quickly PD responds to shocks.
Score-based logistic calibration
Logistic PD models map a score to probability using calibrated coefficients and a consistent default definition. If slope b rises from 0.003 to 0.005 for the same score, the implied PD can move by multiple basis points, affecting pricing and cutoffs. Teams monitor population stability and back-testing metrics such as AUC and Brier score, recalibrating when drift exceeds thresholds.
Governance and reporting outputs
CSV and PDF summaries support audit trails by capturing inputs, intermediate values, and assumptions at calculation time. Use consistent horizons, document recovery conventions, and record parameter sources. For oversight, compare methods on the same obligor set to detect drift and outliers. A practical monthly workflow is to refresh data, recompute PDs, and review changes above 50 bps with stakeholders.
FAQs
1) What does PD represent in this tool?
PD is the probability of default over the displayed horizon or basis. It is not a loss amount and does not include recovery or exposure unless you combine it with other models.
2) Why do different methods give different PDs?
Each method uses different inputs and assumptions. Historical uses observed defaults, hazard uses spreads and recovery, structural uses assets and volatility, and logistic uses calibrated coefficients. Differences are expected, especially across horizons.
3) How is the Plotly curve constructed?
The chart converts the computed PD into an implied constant hazard rate, then plots PD(t)=1−e^(−λt). It is a visualization aid, not a full term-structure model.
4) Should I use annualized or multi-year PD for decisions?
Use the horizon that matches your decision: pricing often uses one-year PD, while provisioning and capital planning may require multi-year PD. Keep the same horizon when comparing borrowers.
5) Can I rely on spread-based PD for private borrowers?
Spread-based PD works best when spreads reflect liquid market pricing. For private names, spreads may be unavailable or noisy, so historical or score-based approaches are typically more stable.
6) What inputs most affect structural PD?
Leverage (V/D), asset volatility σ, and horizon T usually dominate. Higher leverage or volatility increases PD, while higher asset value relative to debt decreases it. Sensitivity tests help quantify impact.