April 2023 Question 8(i)

[Heena]

In this question in order to arrive at discounted reserves my approach was different from the examiner report.

Step 1 - Derived a cumulative payment pattern from the cumulative development factors (1/cdf) .
Step 2 - Converted them into incremental payment pattern .
Step 3 - Calculated the discount rates (same as examiner report)
Step 4 - Calculated IBNR (Ultimate - Paid ) for all years.
Step 5- for every year I calculated: (Sum of IBNR for all years )* discount rate (year (eg. 2022) )*(payment pattern (eg2022)).
Step 6- Took sum of all the cells ( with this formula applied to each year) and arrived at 361 as my discounted reserve.

Can anyone please suggest would this methodology work?

 

[Darren Michaels]

Hi Heena

If I have understood your approach correctly, then I think there may be a slight flaw in step 5. It sounds like you are assuming that the same incremental payment percentage (of ultimate) is paid in a given calendar year for all accident years, which isn't quite correct.

Remember, at any one point in time, each accident year will be at a different stage of development and so the proportion of the ultimate for that accident year paid in a given calendar year will vary. So, for example, at the end of 2021, the 2021 accident year is only 1 year developed, whereas the 2020 accident year is 2 years developed and so on.

Also, if you are working with the payment pattern, then these are usually percentages of ultimate, so you need to multiply by the ultimate for each accident year and not just the reserve (although it depends on how you have calculated / expressed them - I don't have enough information from your description above to tell).

This probably explains why you obtained a slightly different answer to that shown in the Examiners' Report.

Apart from that, it sounds like most of your method is pretty sensible, so you should still have received a reasonable proportion of the available marks.

Apologies, if I have misunderstood your description above, so please feel free to clarify further if that is the case.

One other small thing to note throughout your description is that (ultimate - paid) is strictly the reserve and not just the IBNR as it will also include an estimate of the outstanding reported claims.

 

[Heena]

Hi Darren ,
Thank you so much for you reply.
When you say same incremental payment percentage ,are you referring to a fixed percentage?

Because in my solution for e.g.

year cdf payment pattern (1/cdf) incremental pp discounted reserve
2017 1 100% 13% 400*0.984*13%
2018 1.15 87% 21% 400*0.942*21%
2019 1.50 66% 36% 400*0.895*36%
2020 3.31 30% 23% 400*0.843*23%
2021 13.25 8% 8% 400*0.796*8%
=361

Is this right or respective year's ultimate should have been added ?
or any other changes in this which might help get the right answer?
Sorry for the trouble!

 

[Darren Michaels]

Hi Heena

I am afraid that the calculation above does not look correct to me.

You need to work with the reserves (or ultimates by accident year) not just the total reserve of 400. For each accident year, you have to work out what amounts will be paid in each future calendar year, ie 2022, 2023, 2024, etc

You can then add up the amounts paid in each future calendar year from all accident years (in other words the diagonals of the future triangle) and then discount them back to 31 December 2021 accordingly using the spot yields provided.

The calculation is set out in more detail in the ASET.

 

[Heena]

Okay Thanks Darren!