PD2 Calculator (Two-Year Probability of Default)
Estimate cumulative default risk over a chosen time horizon using a one-year Probability of Default (PD), plus optional Expected Loss inputs.
Model assumes constant annual PD and independent yearly default events for the compounding approximation.
What Is a PD2 Calculator?
A PD2 calculator helps you estimate cumulative default risk over two years (or more). In credit risk, many people start with a one-year probability of default, but portfolio decisions often require a longer horizon. This tool bridges that gap quickly and clearly.
Instead of simply doubling your one-year PD, the calculator compounds risk over time. That matters because once an obligor defaults, it cannot default again, so each period should be treated as survival-then-default rather than a simple linear add-up.
Formula Used in This Calculator
Cumulative Probability of Default
The calculator uses:
Cumulative PD over N years = 1 - (1 - PD1y)N
- PD1y: one-year probability of default (decimal form)
- N: number of years
Expected Loss (Optional Output)
If you provide Exposure at Default (EAD) and Recovery Rate, the calculator also estimates cumulative Expected Loss:
Expected Loss = EAD × Cumulative PD × LGD, where LGD = 1 - Recovery Rate.
How to Use the PD2 Calculator
- Enter your one-year PD in percent (for example, 2.5).
- Set the time horizon (2 years for PD2, or another value if needed).
- Add Recovery Rate and EAD to estimate monetary loss.
- Click Calculate PD2 to view cumulative PD, survival probability, hazard rate, and expected loss.
Example
Suppose a borrower has a one-year PD of 3%, and you want a two-year view. The two-year cumulative PD is:
1 - (1 - 0.03)2 = 5.91%
Notice this is less than 6.00% (which you'd get by just doubling), but close enough to show why compounding is important for cleaner analysis.
Interpreting the Results
Cumulative PD
This is your estimated chance of default at least once within the selected horizon.
Survival Probability
This is the chance the borrower does not default across the full period. It equals (1 - PD1y)N.
Annualized Hazard Rate
The hazard rate translates default probability into a continuous-time intuition and is useful for comparing risk assumptions across models.
Expected Loss
Expected loss combines frequency (PD), severity (LGD), and size (EAD). It's useful for provisioning, pricing, and portfolio-level stress conversations.
Common Mistakes to Avoid
- Using percentage values as decimals (or vice versa).
- Assuming multi-year PD is exactly one-year PD times years.
- Ignoring recovery assumptions when discussing risk in dollar terms.
- Applying the same PD to every borrower without segmentation by rating, industry, or collateral profile.
FAQ
Is PD2 always just two times PD1?
No. PD2 is a compounded probability, not a straight multiplication.
Can I use this for horizons longer than two years?
Yes. Change the time horizon input to any positive whole number of years.
Is this a regulatory model?
No. This is a practical calculator for analysis and planning. Regulatory capital frameworks may require more advanced transition matrices, term structures, or macro overlays.
Bottom Line
This PD2 calculator gives you a fast, transparent way to move from one-year default risk to a multi-year perspective. It is especially useful for credit analysts, risk managers, lenders, and business owners who want a cleaner view of potential loss over time.