The Loss Development Method

The loss development method, also known as the chain ladder method, is the most widely used approach for estimating healthcare IBNR reserves. It works by observing how past claims developed over time and projecting that pattern onto more recent periods.

This page covers the technical steps of the loss development method in detail.

Here’s the process at a high level:

Step 1: The Lag Triangle#

Two dates are central to reserving: the incurred date (i.e. service date) and the paid date. The incurred date is when the medical service was provided to the member. The paid date is when the insurer paid the corresponding claim. For example, a surgery performed in January may not result in a payment until May.

This time difference between the incurred date and the paid date is what creates the need for IBNR reserves.

The difference, typically measured in months, between the incurred date and the paid date is called the lag. Conventionally, the lag can start at either 0 or 1. When using IBNR.net, the lag starts at 0, as we feel that this definition more intuitively aligns with the definition of months between the paid date and incurred date. In some other models, the lag can start at 1 when the incurred date is equal to the paid date.

A lag triangle is the foundation of the loss development method. It arranges claims data into a grid where one axis represents the incurred date and the other axis represents the paid date. A lag triangle does not need to be a square matrix. If there are more paid dates than incurred dates, the difference between the most recent paid date and the most recent incurred date is called the run-out. For example, if incurred dates range from January 1st, 2025 to December 31st, 2025, and paid dates range from January 1st, 2025 to March 31st, 2026, the run-out is 3 months.

For standardization purposes, on IBNR.net, the data is stored such that:

• Rows represent when the claim was incurred.
• Columns represent when the claim was paid.

Triangles can also be represented with the paid date on the rows and the incurred date on the columns. Triangles uploaded in this format will automatically be inverted as part of the standardization process.

Let’s take a look at an example of a lag triangle.

Notice how the grid is split along the diagonal, creating a triangle shape. Claims cannot be paid before they are incurred, so the values in the lower-left corner are all zeros.

Observing this particular triangle, we see that most claims are paid in the same month as they’re incurred (lag 0). Paid amounts slowly decrease in the following lags, until they eventually reach a negligible amount.

A triangle that approaches zero more quickly is described as “completing fast” or having a “short tail.” Conversely, a triangle that takes longer to approach zero is said to “complete slowly” or have a “long tail.” The tail length is important because it directly affects how much uncertainty exists in the IBNR estimate. Longer tails mean more unpaid claims remain outstanding at any given point, making the reserve estimate less certain.

In general, healthcare claims complete fast, typically over the course of months rather than years, so advanced statistical models designed for analyzing long-tailed exposures are rarely necessary.

Different service categories complete at different speeds. For example:

• Pharmacy claims tend to complete the fastest. Prescriptions are typically adjudicated electronically at the point of sale, so the lag between incurred and paid dates is very short, often within the same month.
• Outpatient claims (e.g. office visits, lab work, imaging) complete at a moderate pace. These claims require submission and processing but are generally straightforward, with most payments settling within one to three months.
• Inpatient claims (e.g. hospital stays, surgeries) tend to have the longest tails. These involve higher dollar amounts, more complex billing, and often require additional review or negotiation before payment is finalized. It is not uncommon for inpatient claims to take several months or longer to fully settle.

Because of these differences in completion speed, actuaries typically build separate triangles for each service category rather than combining all claims into a single triangle. Mixing fast-completing and slow-completing categories would obscure the underlying development patterns and reduce the accuracy of the resulting IBNR estimate.

Different populations may also complete at different speeds. For these reasons, actuaries often build separate triangles for distinct populations, such as by line of business, plan type, or region, to ensure that each triangle reflects a homogeneous development pattern. Combining populations with materially different completion speeds into a single triangle can distort the development factors and produce unreliable IBNR estimates.

Ultimately, the choice of triangle cuts is a judgment call based on the available data and the needs of the analysis. Fortunately, IBNR.net simplifies the process by allowing for the immediate generation of triangles by uploading a single column-wise dataset, with the first three columns representing the incurred date, paid date, and paid amount, and each column representing an additional triangle filter, such as service category, population, or other relevant criteria.

Step 2: The Cumulative Triangle#

The cumulative triangle converts the incremental lag data from Step 1 into running totals. Each cell equals the sum of all incremental values in that row up to and including that column, representing the total amount paid through each subsequent period.

Consider the January 2021 row. The first cell is 2,140, the amount paid in the same month claims were incurred. By the second column, the cumulative total reaches 2,140 + 1,552 = 3,692, reflecting all payments for January 2021 claims through February. By the final column, the total reaches 4,855, the full amount paid for that incurred month across the entire year.

The critical observation is that older rows (such as January) are nearly complete, with the vast majority of claims already paid. More recent rows (such as December) remain in the early stages of development. The cumulative triangle provides a clear view of each incurred month’s maturity, allowing for easier comparison and set-up for the next steps.

Step 3: Development Factors#

Development factors, also called age-to-age factors or link ratios, quantify the rate at which claims grow from one period to the next. Each factor is calculated by dividing a cumulative value by the immediately preceding cumulative value in the same row.

For example, in the January 2021 row:

• Lag 1 = 3,692 / 2,140 = 1.72523, meaning claims grew by approximately 72.5% between the first and second periods.
• Lag 2 = 4,281 / 3,692 = 1.15953, reflecting an additional 16.0% growth in the subsequent period.

As claims mature into later lags, the factors converge toward 1.0, reflecting the diminishing volume of remaining unpaid claims.

Note the triangular shape. Each row has one fewer factor than the row above it, since two consecutive cumulative values are required to compute a ratio.

The development factors along each column (lag) are of primary interest. Lag 1 factors indicate how much claims typically grow between the first and second periods, Lag 2 factors capture growth between the second and third periods, and so on. The degree of consistency within each column reflects the stability and predictability of the underlying runoff pattern.

Note that Lag 0 is not included in the development factors, as there is no denominator for the Lag 0 calculation. This naming convention may also explain why some models define the lag as starting at 1 instead of 0, with the “1” representing the denominator of the ratio rather than the numerator.

Development factors can inform the user about the suitability of the loss development method for the data in question.

• If age-to-age ratios are highly variable for a given lag, that could indicate that the loss development method is not a suitable method for the population in question.
• If later lags don’t converge to 1, that can indicate that claims have not yet settled, and the historic data may not be suitable for the loss development method.

In either of these cases, other methods may need to be used, either in conjunction with the loss development method, or separately altogether.

Step 4: Selecting an Average Method#

Individual development factors can exhibit volatility; a single large claim or a processing delay can distort a given period’s ratio. To produce a more stable estimate, the factors within each lag column are averaged.

Several averaging approaches are available. A simple average assigns equal weight to every factor in the column. A medial average excludes the highest and lowest values before averaging, reducing the influence of outliers. The sample can also be restricted to a specified number of recent periods (e.g., last 6) to place greater emphasis on recent experience.

Below are three different averaging methods, each with a different sample size and different approach to handling outliers.

We observe that all three methods yield similar results, indicating that the data could be relatively stable and predictable. For this example, a Simple Average of the Last 6 periods is selected.

The choice of averaging method represents one of the most significant actuarial judgment decisions in the reserving process, especially when anomalies are present. Different methods can yield materially different IBNR estimates, and actuaries typically evaluate multiple approaches before applying professional judgment to select the most appropriate one.

Step 5: Age-to-Ultimate Factors#

Age-to-ultimate factors indicate the total expected growth from a given lag period to the point at which all claims are fully settled. They are calculated by multiplying the selected average factors from the current lag through the final lag.

For Lag 1, the age-to-ultimate factor is the product of all selected average factors:

1.3842 × 1.2291 × 1.0914 × 1.0114 × 1.0074 × 1.0045 × 1.0031 × 1.0024 × 1.0032 × 1.0008 × 1.0004 = 1.9192

For Lag 2, the age-to-ultimate factor is the product of the selected average factors from Lag 2 onward:

1.2291 × 1.0914 × 1.0114 × 1.0074 × 1.0045 × 1.0031 × 1.0024 × 1.0032 × 1.0008 × 1.0004 = 1.3865

This indicates that claims at Lag 1 are expected to grow by a factor of 1.92 before reaching their ultimate value. At Lag 11 (the most mature), the factor is 1.0004, indicating that those claims have essentially completed their development.

Step 6: Completion Factors#

The completion factor is the reciprocal of the age-to-ultimate factor (1 / age-to-ultimate). It represents the proportion of ultimate claims that have been paid at each lag.

For Lag 1: 1 / 1.9192 = 0.5211, indicating that approximately 52.1% of claims have been paid after one period. For Lag 11: 1 / 1.0004 = 0.9996, indicating that claims are virtually fully developed.

Completion factors provide an intuitive measure of maturity. A completion factor of 0.62, for instance, indicates that approximately 62% of the ultimate cost for that incurred period has been paid, with the remaining 38% outstanding as IBNR.

Step 7: Determining IBNR Reserves#

The final step brings all prior calculations together. For each incurred month, the total amount paid to date is divided by the completion factor to estimate the ultimate cost, and the paid amount is subtracted to derive the IBNR reserve.

The formula is:

Ultimate = Total Paid / Completion Factor

IBNR Reserve = Ultimate - Total Paid

To illustrate, consider claims incurred in September 2021. A total of $5,886 has been paid through the valuation date. That month is at Lag 4, with a completion factor of 0.9675, indicating that approximately 96.8% of claims have been paid. Dividing $5,886 by 0.9675 yields an estimated ultimate of $6,084. The difference, $198, represents the IBNR reserve for that month.

Older incurred months carry small or zero IBNR, as the majority of claims have already been paid. More recent months carry larger IBNR reserves, as they remain in the earlier stages of development. December 2021 has the largest IBNR at $1,770, with only 52.1% of its expected claims paid after one month.

In aggregate, $61,082 has been paid, while the estimated ultimate cost is $65,422, resulting in a total IBNR reserve of $4,340. This amount must be recognized on the balance sheet to cover claims that remain in the payment pipeline.

Wrapping Up#

The loss development method derives its strength from a straightforward premise: observe how claims have developed historically, average those patterns, and project them onto more recent periods. However, the apparent simplicity of the framework should not be mistaken for a lack of complexity in its application. The actuarial judgment required at each stage (selecting the averaging method, determining the number of periods to include, and deciding whether to adjust for anomalies) is what distinguishes a mechanical calculation from a well-reasoned reserve estimate.

Although IBNR.net automates the mechanical calculations for you, it is still important for the user to understand the process and the assumptions behind the loss development method. Understanding the foundations of the reserving process will allow for more informed decisions.

This guide has covered the foundational concepts. In practice, actuaries typically incorporate additional considerations such as seasonality, trend calculations, credibility weighting, margin, and other refinements. Each of these techniques builds upon the framework presented here.

Disclaimer: This article is a work in progress and reflects the opinions of Jeff Yang, FSA at IBNR.net. It is intended for educational purposes only and should not be relied upon as the sole basis for professional decisions. Readers should exercise independent judgment when making actuarial or financial decisions. Please contact support@ibnr.net if you have feedback or identify any mistakes on this page.