Notes on the inflation adjusted chain ladder

​I found myself explaining the inflation adjusted chain ladder (IACL) to someone recently, and there was a step in the calc I found difficult to justify to them. It’s the idea that claims inflation in a paid triangle manifests itself on a calendar year basis (i.e. along the diagonals). Perhaps this is what you were always told, but the problem is I just don’t think its necessarily true.

​Inflation adjusted chain ladder

Before we dive in too far, what is the IACL?

The IACL is an extension to the standard chain ladder method which adjusts for claims inflation explicitly rather than implicitly [1]

The high-level steps are:

1. Convert a cumulative paid triangle to an incremental paid triangle
2. Inflate all the incremental payments to a consistent year (typically the most recent calendar year)
3. Convert the triangle in step 2 back to a cumulative triangle
4. Apply a standard chain ladder to the cumulative triangle in step 3 to estimate future payments
5. Then apply an assumption about future inflation to the future payments estimated in step 4

Calendar year inflation

Typically, this technique is taught in such a way that assumes that claims inflation is always a calendar year of payment effect. See the CM2 notes from IFoA for example [2]:

“Claims inflation will affect the payments in the run-off triangle by calendar year of payment.”

And this approach has propagated, for example see the following guidance note from Lloyd’s [3]:

“Future inflation should be considered on a calendar year basis until all claims are run-off to understand the impact on ultimate claims estimates.”

If we go back to the original paper however, by Richards and Cappers[4], the authors are quite clear that one step of their IACL model is “Determine the timing of the inflationary impact. (i.e., accident date, report date, paid date ... etc.)”. They consider it an empirical question whether inflation manifests according to paid date and not some other timing, and this is listed as just one possible option among a few.
​
Hindley in his excellent book, Claims Reserving in General Insurance [1], appears to be quite careful in his wording when writing the section on IACL. He consistently refers to it as a model for explicitly dealing with ‘calendar year’ effects (which is 100% true), he doesn’t refer to this as adjusting for inflation, and he cautions against naively using inflation indices when adjusting.

Why would inflation not be a calendar year effect?

Let’s look at an example from motor own damage.

If your vehicle is involved in a crash and is written off, from a legal perspective in the UK, the amount you are owed is the ‘fair value of your vehicle at the date of accident’. [5]

Let’s compare two claims, both involving identical vehicles.

1 – DOL = 1/10/2019, it is reported 1 week after the accident, the car is a write off, so 1 week later the claimant receives the fair value of the car. Claim closed for £1000 on 14/10/19.

2 – DOL = 1/10/2019, this claim however is reported 2 months late, the insurer disputes it for 4 months, but eventually the claim is paid, lets suppose the claim is not closed until 1/4/2020, but is also closed at £1000. Which was the fair value of the vehicle at the date of accident.

There has been an additional 6 months of inflation between these two dates. However in terms of legal rights, both claimaints are entitled to  the same amount of money.

Our inflation adjusted chain ladder however, would put these two amounts in different development cells, which would be in different calendar years, and then apply whatever our assumed inflation rate was to the 1st claim to bring it on level with the second claim. Obviously this is not correct, and actually for this head of damage technically we should inflate according to accident year, not calendar year.

Now this is where it gets messy. In practice, the amount from claim 2 might drift up. Most claims do not settle in a court, and are instead negotiated, if the fair value of a vehicle has gone up since the loss, this may influence the negotiation.

For other lines of business, this dynamic does play out on a calendar year basis. For example, if the car was not a total loss, but instead needed repair. Then the entitlement would be to the cost of repair, and if repair costs went up between the two dates, then there would be inflation between the different dates of repair. Given the delay in reporting claim 2, this would probably result in a delay to the repair, and inflation coming through.

In this case, we should inflate according to the calendar year of payment. Or strictly speaking, the calendar date of repair, which is likely to be almost the same thing in pratice.

For bodily injury, most components increase over time, and this will also generally be in line with when payments are made.

Really the moral of the story is that each line of business, and each head of damage within the line of business will have a different relationship to inflation and timing. And we can’t just assume that the calendar year version of the IACL is the right one.

How do these nuances get lost as they work their way through the system?

I’m also interested in how these errors propagate, because clearly the original paper by Richard and Cappers, and Hindley’s book are quite precise in their framing.

Most actuaries working today, are not deriving the techniques they are using from first principles, they’re also not reading original research, and to be honest that’s as things should be. Most people do not have the time or interest. Instead, there is a natural pipeline from original published research, which is distilled into course material as either textbooks or notes for actuarial exams, which then is taught and becomes the body of practice that actuaries use.

​What became apparent with IACL is that it became the go-to technique post-covid when we saw an uptick in claims inflation, and most actuaries having not touched it since their exams, basically went back and brushed up on their IFoA notes. Therefore the slight simplifications in the IFoA material, in what was a fairly niche part of the syllabus that hardly anyone was using in practice, suddenly became quite important. 

Claude/LLMs

Claude Opus 4.7, as of April 2026, also explains IACL with reference to the fact that claims inflation is as calendar year effect. Perhaps not surprising given things like the IFoA notes are in the training data.

Interestingly, Claude describes step 2 of the method (inflating the losses) in a slightly quirky way. It refers to ‘deflating to the most recent year’ which I would argue is an incorrect use of the word deflate. It should either say deflate to a base year (in the past), or it should say ‘inflate to most recent year’.

I couldn’t find this particular use of the word deflate in any of the academic papers. But interestingly, I could find a couple of recently written articles which do use the term ‘deflate’ this way, and which also repeat the ‘claims inflation = calendar year effect’ assumption.

You can quite clearly see how for new generations of LLMs, the latest versions of which are going to be trained on those articles for example, are in danger of some form of model collapse, and potentially new content on the internet may become less valuable to them.

How to use IACL properly?

I’d encourage you when using the ICAL method, to go back to Capper and Richard’s initial approach, and to attempt to understand the mechanics of a loss and settlement, and what this implies for how inflation feeds through to the claims triangle. Is the legal entitlement set at date of loss, date of reporting, date paid etc. And how does this legal entitlement play out in practice? It may manifest in your triangle as a calendar year effect, or it may not. It will generally vary by head of damage and line of business, but really we should treat this as an empirical question.

The above example I gave from motor own damage was based on a really interesting chat I had with our head of claims about one of our motor books that made me rethink how I was approaching a particular model. The best actuaries I’ve met, generally don’t use anything more complicated than the basics taught in the exam, but they’re plugged in to everyone else’s expertise in the company, and they use what they know well.
 
  
[1] Claims Reserving in General Insurance – David Hindley (2018)
[2] Subject CM2 Financial Engineering and Loss Reserving Core Principles Core Reading for the 2021 exams
[3] Lloyd’s -Allowing for Inflation in Reserving – August 2022
[4] ‘EVALUATING THE IMPACT OF INFLATION ON LOSS RESERVES’ , Richards and Cappers
[5] ​https://www.financial-ombudsman.org.uk/consumers/complaints-can-help/insurance/motor-insurance/vehicle-valuations-write-offs