SP8 Rating analysis steps

[jack123]

Chapter 19 of the course notes state that in a rating analysis you need to:
1. Project claims to ultimate
2. Project forward to period over which new rates will be charged (allowing for future claims trends)

This order confuses me.
Suppose you have data up to 2024 and that claims take 2 years to develop to ultimate. In your triangle you have the following incremental estimates for a 2024 policy (in nominal values):
2024: 100
2025: 150
2026: 50
The ultimate value would then be 100 + 150 + 50 = 300

My approach
Now if I wanted to price a 2025 policy, I would expect claims to happen in 2025, 2026 and 2027. Therefore I would assume claims are as follows:
2025: 100* (1 + inflation from 2024-2025)
2026: 150* (1 + inflation from 2025-2026)
2027: 50* (1 + inflation from 2026-2027)

The new ultimate value would be 100* (1 + inflation from 2024-2025) + 150* (1 + inflation from 2025-2026) + 50* (1 + inflation from 2026-2027)

The approach in the notes?
The notes suggest projecting to ultimate and then multiplying by one year's inflation (presumably from 2025-2026). This would give an ultimate of 300*(1 + inflation from 2025-2026)

But this is not the same.

Why in the notes do we bother calculating an ultimate value before adjusting for inflation? Surely we should adjust incremental payments for inflation in the new rates period before summing to get an ultimate value?

 

[MrLiu]

Others correct me if I'm wrong.
I don't 100% know but I guess the 2024 and prior years ultimate have already allowed for the future inflation as you described. And the amounts are in 2024 terms.
What is missing is push everything including the future inflation allowance out for another year so everything is in 2025 terms.
Doing as you suggested would cause some degree of double count.
It's a good question, hopefully one of the tutors can clarify.

 

[Ian Senator]

Yes, it all depends on what your tabulated figures have already allowed for, and also your development pattern which may or may not have been adjusted for inflation too. In practice, in the exam, any reasonable method would normally be acceptable as long as you state your assumptions and methodology, and don't over-simplify too much (eg by assuming zero inflation throughout!).

 

[jack123]

Hi both, thanks for the responses, but my question is not regarding double-counting. I understand that you need to apply inflation to get from 2024-2025. What I am confused about is that if you first calculate ultimates for a 2024 policy then multiply that by (1 + inflation from 2024-2025) you won't get the ultimate for a 2025 policy

 

[Katherine Young]

Your approach is more detailed than that in the course notes, in that you're considering separately the amounts paid in each year of run-off.

The method in the course notes (and the method that tends to be used in the exam) is a simplification of this. It inflates from the average payment date under the old rates, to the average payment date under the new rates.

So you're correct that the methods aren't the same, but if inflation is near constant it shouldn't make much difference.

Ian is right though, in the exam, any reasonable method would normally be acceptable as long as you state your assumptions and show your method clearly.

 

[jack123]

Oh I see, thank you!