Bornhuetter-Ferguson Reserve Calculator
The Bornhuetter-Ferguson method stabilises reserves for immature accident years by blending an a priori expected loss with actual development. The IBNR reserve equals the expected ultimate loss times the proportion still unreported, where the unreported share is one minus the reciprocal of the cumulative development factor. The ultimate is then paid claims plus that reserve, so a low or high early paid figure does not whip the estimate around. This calculator takes paid claims, the expected loss, and the development factor as user-editable inputs and returns the unreported percentage, reserve, and ultimate.
Bornhuetter-Ferguson formula
Percent reported = 1 / cumulative development factor
Percent unreported = 1 - (1 / cumulative development factor)
BF reserve = expected ultimate loss * percent unreported
BF ultimate = paid claims + BF reserve
BF anchors the unpaid piece to the expected loss rather than to the leveraged actual, which is why it behaves well for immature years.
Bornhuetter-Ferguson context
- BF blends an a priori expected loss with the development pattern.
- It is preferred for recent, thinly developed accident years.
- As a cohort matures, BF and chain ladder converge toward the same ultimate.
- The expected loss usually comes from premium times an expected loss ratio.
- Casualty Actuarial Society materials describe the method and its assumptions.
Bornhuetter-Ferguson: frequently asked questions
What is the Bornhuetter-Ferguson method?
Bornhuetter-Ferguson (BF) is a loss-reserving method that blends an a priori expected loss with actual development. The reserve equals the expected ultimate losses times the proportion still unreported. The ultimate equals paid claims plus that reserve. BF is more stable than chain ladder for immature accident years.
How does BF differ from chain ladder?
Chain ladder leverages the actual paid amount by the development factor, which is volatile for green years. BF instead applies the unreported percentage to a separate expected-loss estimate, so a low or high early paid figure does not swing the reserve. Paid claims still enter through the ultimate.
Where does the expected loss come from?
Typically expected losses equal earned premium times an a priori expected loss ratio, or a plan or pricing estimate. Because it depends on your book, the expected loss is a user-editable input here rather than an assumed figure.
What is the unreported percentage?
It is one minus the reciprocal of the cumulative development factor: 1 - 1/CDF. The reciprocal of the CDF is the percent reported (developed), so the complement is the percent still to emerge, which BF applies to the expected loss.
When is BF preferred?
For recent, immature accident years where little has been paid and chain ladder would be unstable, and for new lines with limited history. For mature years where development is nearly complete, chain ladder and BF converge.
Official sources
- Casualty Actuarial Society: CAS reserving methods literature.
- National Association of Insurance Commissioners: NAIC loss reserve standards.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.