Incurred But Not Reported (IBNR) Liability Explained

Motivation

A lag triangle is a table that shows how medical claims are paid over time. Rows usually represent the month care was received, called the incurred month. Columns show how many months later the claims were paid, called the lag or development month.

This matters because medical claims are not paid all at once. A member may receive care in January, but the provider might submit the claim weeks later, the TPA processes it after that, and payment may not happen until February, March, or later.

IBNR means incurred but not reported, though in medical reserving it often means broader unpaid claim liability: claims that have happened but are not fully paid yet.

IBNP stands for Incurred but not paid. As opposed to IBNP, which captures the unknown or not yet reported claims, IBNP captures the known and recorded claims. IBNP is typically expressed as IBNP = Case Reserves (Known & unpaid) + IBNR (Unknown & unpaid). Since our portal is designed to record ledgered claims, we do not have the capabilities to fully report IBNR for now.

But for the purpose of this guide, we will use IBNP and IBNR interchangeably.

For a self-funded medical plan, this is important because the employer, not an insurance carrier, ultimately pays the claims. The TPA administers the plan, processes claims, and provides reporting, but the claim liability belongs to the self-funded plan sponsor.

So IBNR answers a practical finance question:

How much money should the employer expect to pay for care that has already happened, even if the bills have not fully arrived or been paid yet?

That estimate matters for:

Chain Ladder Explained

Chain ladder is a way to estimate unpaid claims using the payment pattern already visible in historical claims data.

The basic idea:

If older claim months usually grow from $100 paid to $120 paid as they mature, then newer claim months probably need similar growth.

That growth pattern is called development.

1. Start with Incremental Paid Claims

This is what was paid in each lag month.

Each row is a claim month. Each column is how many months later the payment happened.

2. Convert to Cumulative Paid Amounts

Chain ladder uses cumulative paid, not incremental paid.

E.g., Jan Age 1 = 100 + 80 = 180

This table shows how claims grow as they mature.

3. Calculate Age-to-Age Factors (aka Link Ratios)

An Age-to-Age factor (aka link ratio) measures growth from one age to the next.

Formula: Age 0 to Age 1 ratio = Age 1 cumulative / Age 0 cumulative

• Average selected factor: (1.80 + 1.75 + 1.77) / 3 = 1.7733

• So we select: Age 0→1 factor = 1.7733

Meaning: On average, claims at age 0 grow by 77.33% by age 1.

4. Build Development Factors

Repeat that for every age.

These are the claim growth assumptions.

5. Convert to Cumulative Development Factors (CDF)

A cumulative development factor (CDF) answers the question:

If a month is currently at this age, how much do I multiply paid-to-date by to estimate ultimate claims?

6. Estimate Ultimate Claims

Now apply the CDF to each row’s latest paid amount.

Formula: Ultimate = Latest Paid × CDF

7. Calculate IBNP, the unpaid estimate

Formula:

IBNP = Ultimate - Paid to Date

So the chain ladder estimate says: We have paid $800 so far, expect $978 ultimate, and need $178 of IBNP.

TL;DR

At the end of the day, Chain ladder is simply:

1. Turn incremental paid into cumulative paid.

2. Measure how older months grew from one age to the next.

3. Average those growth ratios.

4. Multiply remaining growth into CDFs.

5. Apply CDFs to newer months.

6. IBNP equals ultimate minus paid.

The method works best when the past payment pattern is a reasonable guide for the future.

Appendix A - The Bornhuetter-Ferguson Method

Chain ladder trusts the paid-to-date number completely. If April has only $140 paid at Age 0, chain ladder multiplies it by 2.01 and calls that the answer.

That is problematic for young months since a single large claim (or other changes) can swing the estimate.

Bornhuetter-Ferguson (B-F) fixes this by blending two things:

1. What the plan expected to pay for that month before any claims came in.

2. What the payment pattern says is still unpaid at the current age.

The basic idea:

If we expected April to cost $250, and history says only half of a month is paid by Age 0, then about half of $250 is still to come. What has actually been paid so far does not change that.

What changes

Assuming an ultimate expected of $250, step 7 using the B-F method:

Compared to the traditional Chain ladder method, B-F lowered IBNP from $178 to $162 and the difference is almost entirely in April since the month is 50% unpaid.

Pros and cons

BF works best when the plan has a good budget or PMPM estimate and the recent months are too young to trust.

Appendix B - Benktander Method

Chain ladder trusts the $140 paid completely. B-F trusts the $250 budget completely for the unpaid half. Benktander serves as a hybrid and blends the two.

The mechanic is one extra step. Take the B-F ultimate, treat it as a better budget, and apply the percent unpaid one more time.

Formula: Benktander IBNP = B-F Ultimate × Percent Unpaid

E.g., Apr IBNP = $266 × 50% = $133.

=> Apr Ultimate = $140 + $133 = $273.

Why the answer lands in the middle

Benktander is a weighted average of the traditional Chain Ladder and B-F method (where the weight is the percent paid)

Benktander IBNP = (Percent Paid × Chain Ladder IBNP) + (Percent Unpaid × B-F IBNP)

So the difference between B-F and Benktander is who decides:

• B-F: the budget decides the whole unpaid part, at every age.

• Benktander: the budget decides in proportion to how much is still unpaid. At Age 0 it is a 50/50 split. By Age 2 the paid data has 97% of the vote.

As a month ages, Benktander slides from the budget toward the real data on its own. BF never does. Chain ladder never used the budget to begin with.

Pros and cons

Benktander works best when the plan has a budget but does not fully trust it, and wants one method that behaves well for both new and old months.