Visual summary
Calculator
Example data table
| Accident Period | Reported Losses | Selected Factor | Implied Ultimate | Implied IBNR |
|---|---|---|---|---|
| 2025-Q1 | PKR 1,250,000 | 1.35 | PKR 1,687,500 | PKR 437,500 |
| 2025-Q2 | PKR 1,480,000 | 1.22 | PKR 1,805,600 | PKR 325,600 |
| 2025-Q3 | PKR 1,610,000 | 1.12 | PKR 1,803,200 | PKR 193,200 |
Example values are illustrative and not guidance.
Formulas used
- Development factor: Ultimate = Reported × Factor; IBNR = Ultimate − Reported.
- Expected loss ratio: Ultimate = Earned Premium × ELR; IBNR = Ultimate − Reported.
- Bornhuetter‑Ferguson: IBNR = EP × ELR × (1 − % Reported); Ultimate = Reported + IBNR.
- Approx. interval (optional): σ ≈ |IBNR| × CV; Range = IBNR ± zσ.
How to use this calculator
- Select a method that matches your data maturity.
- Enter reported losses, then the method-specific fields.
- Optionally add CV and a z‑score for an interval.
- Press Submit to view IBNR and ultimate estimates.
- Use Download CSV or PDF for sharing and audit trails.
IBNR as a reserve component
IBNR reflects claim cost that has occurred but has not entered the reported inventory. For short-tailed lines, reporting can exceed 85% by month three. For long-tailed liability, the same point can be below 40%, making reserve adequacy sensitive to emergence. A check is the reported-to-ultimate ratio against case reserves.
Choosing a development factor
Development factor methods translate reported losses into an ultimate estimate using a selected factor from experience. A factor of 1.35 implies 74.07% is reported, while 1.12 implies 89.29% is reported. Small factor changes materially move IBNR when reported is large. If reported is 10,000,000, moving from 1.25 to 1.30 increases ultimate by 500,000 and increases IBNR by the same amount.
Expected loss ratio benchmarking
Expected loss ratio approaches start from earned premium and apply an expected loss ratio, such as 62.5%, to form an ultimate target. If premium is 5,000,000 and ELR is 62.5%, expected ultimate is 3,125,000. IBNR then equals expected ultimate less reported. When reported is 2,400,000, the implied IBNR is 725,000, and the implied loss ratio to date is 48.0%.
Bornhuetter‑Ferguson blending
Bornhuetter‑Ferguson blends stability from an ELR with responsiveness from reported activity. When 70% is reported, the unreported share is 30%, so IBNR equals EP × ELR × 0.30. This reduces volatility for immature periods compared with pure development factors. For the same 5,000,000 premium and 62.5% ELR, the a‑priori unreported component is 937,500 when 50% is unreported.
Intervals and communication
Point estimates are useful, but stakeholders often want uncertainty framing. Using a coefficient of variation of 25% and a 95% z of 1.96 gives a simple range around IBNR. For an IBNR of 437,500, sigma is 109,375 and the range is roughly 223,125 to 651,875. Use ranges to compare scenarios, not to replace governance; document why a higher CV may be needed for periods.
Audit-ready outputs
Reserve workflows benefit from documentation. Exporting the selected method, inputs, and rounded outputs supports review and change tracking. Use CSV for aggregation across periods, and PDF for single-period sign-off, especially when assumptions change quarter to quarter. A control is to store the run date, parameter set, and resulting ultimate, then reconcile any movement to changes in reported, factors, or ELR assumptions.
FAQs
What does IBNR measure in practice?
It estimates the portion of ultimate claims cost not yet reported or recorded. It supports reserve setting, profitability monitoring, and comparisons across accident periods with different reporting maturity.
When is the development factor method preferred?
It works best when credible historical development patterns exist and operational reporting is stable. It can be less reliable for new products, changing claims practices, or shock events that alter emergence.
How should I pick an expected loss ratio?
Use pricing indications, recent calendar-year experience, exposure changes, and any known shifts in mix or severity. Document the rationale and update the ratio when rate, trend, or underwriting changes occur.
Why use Bornhuetter‑Ferguson?
It reduces early volatility by relying more on an expected ultimate while still responding to reported data. It is commonly used for immature periods where pure development can overreact.
Is the interval output a formal confidence interval?
No. It is a quick approximation based on a user-supplied variation level and a normal z-score. Formal intervals typically require stochastic reserving models and diagnostics.
Can IBNR be negative?
Yes, if reported losses exceed the selected ultimate estimate. That situation often signals conservative case reserving, unusual large claims, or assumptions that need review before conclusions are drawn.