Q&A Bank Part 6

[Cheng]

Hi! I'm a little confused with the solution for qs 6.1iii and 6.4ii

Qs6.1iii)
For qs6.1iii, to derive the loss ratio from historical experience, we need to obtain the on-level premium and claims data. And to derive the on-level premium, we need to adjust for rate change for the period covered and for the period being priced.

I would like to confirm that on-level premium is referring to the premium at current date value, i.e. we would adjust the past premium to get the present day value? and what's the difference between period covered and period being priced?

Qs 6.4ii)
1) Is it true that burning cost is referring to the actual cost, regardless of whether it has been paid or not?

2) I don't really get why we need to make the following assumptions and how does that impact the calculations of burning cost:

- business is written evenly over the year, therefore adjust the data by 6 months to reflect unexpired risks (which data do I adjust?)

- hence, the average UY claim occurs at the end of UY, ie 31/12
(how do we come to this assumption? and why do we need this assumption given that we already know the exact date of loss being reported/paid?)

3) Also, when adjusting for claims inflation, I would need to adjust from the reported date of the loss up to 31 Dec of Y6 (because on average, claims occur mid of Y6 and paid at the end of Y6)? and that is how we get 5 years 7 months and 27 days for top risk?

thanks in advance!

 

[Katherine Young]

Q6.1(iii)

I would like to confirm that on-level premium is referring to the premium at current date value

We need to adjust the historic loss ratio to make it relevant to the claims that will arise from the future period of cover. So if premiums have increased by 5% (say) since the time period to which the historic loss ratio relates, then we would have to divide by 1.05.

What's the difference between period covered and period being priced?

No difference. (I agree that the solution is a little confusing in this respect. We’ll change this for next year.)

The solution is simply saying that we just need to adjust the loss ratio for changes in premium / mix of business / claims ...

from:

the time period to which the historic loss ratio relates ...

to:

the time period to which the future loss ratio will apply.

Q6.4(ii)

why do we need assumptions, given that we already know the exact date of loss being reported/paid?

The claims data provided relates to historic losses. We need to adjust these to estimate the sorts of claims that might occur under the XL contract for underwriting year 6.

How do we come to these assumptions?

If we assume that business written in UW year 6 will be written evenly over the year, then the average policy will be written half way through the year. If we further assume that risk is earned evenly over a policy year, then the average claim on the average policy will occur 6 months later. This is what the solution means when it says “adjust the data by six months”; ie we are inflating the claims data to 31/12/year 6.

I would need to adjust from the reported date of the loss up to 31 Dec of Y6 (because on average, claims occur mid of Y6 and paid at the end of Y6)?

Not quite. On average, claims occur at 31/12/year 6. The reasoning for this is as per (2) above. The solution assumes no reporting / settlement delay.

 

[Phillax]

Hi Katherine,

In reference to your last point above here - I have also been confused on this question. Why do we inflate from the Claim Reported date not the Claim Payment date? My understanding is that you always inflate from the past payment date to the future expected payment date?

The solution assumes no reporting delay, which is fine, but does not mention assuming no settlement delay. If it was assuming no settlement delay, (ie no delay between a claim reported and it being paid) then I suppose it would make sense to inflate from the outstanding date. But seeing as we have several claims, each with significant settlement delays, this assumption would not be a sensible one? It also doesn't fit well with what you'd expect in real life?

Or are we deciding to assume no settlement delay, even if it's a dubious assumption, because otherwise we'd struggle to inflate the past claims that have not yet being paid? In which case another acceptable solution (which would perhaps show more understanding) would have been to take some kind of average payment delay and use this?

I'd appreciate you clearing this up, as it had me very confused this morning!

Many thanks,
Phil

 

[Katherine Young]

Hi Phil,

Usually you would inflate claims from the date of payment to the average payment date during the period to which the new cover will apply. This is consistent with what you have said.

Often though, there is assumed to be no settlement delay. If this assumption holds, inflating using reporting dates will be fine.

Now, your point is that the claims data in this question do exhibit settlement delays.

However, if inflation remains stable, and settlement delays remain stable, it will make no difference. We'll be inflating by the same amount, but just shifted along by six months say.

Let's take an example. If a historic loss was reported on 1/1/year 1 and paid on 30/6/year 1, then we have a choice:

1) We can either inflate from the reporting date 1/1/year 1 to the average future reporting date 31/12/year 6 (which assumes no settlement delay)...

2) ... or we can inflate from the payment date 30/6/year 1 to the average future payment date 30/6/year 7 (which assumes no changes to the settlement delay of 6 months).

In both cases, we inflate for 6 years, and the estimate will be unchanged.

Kind regards,

Katherine.

 

[Phillax]

Thanks Katherine. I suppose in which case it would be good to also write down the assumption that settlement delay is unchanged.

 

[Katherine Young]

Indeed!