Reinsurance arrangement calculations - suplus and XL cover's

September 2002 - Q7

In this question, I would have though you first calcuate for the surplus arrangement, the amount ceded via the max retention level and the EML. so for risk 2, the max retention is 500 and the EML is 2500 so therefore the claims would be split 500/2500 and 2000/2500?
Since the max no of lines the reinsurer would accept (4*L = 4* 500) then the max they can accept is 2000. (and not 2739 as the solution says?)

Also when moving onto the XL arrangements - even though it says these arrangement happen in the order given, it looks like both XL arrangements are calculated on the net of the surplus arrangement? so in that case, the amount C pays, isnt net of the claim after B falls into place? - is this the way XL happens always? so we sort of group the different types of treaties together and go net of these at each diff stage?

If the insurer got away with it, could he have the XL arrangements cover his retention in the surplus arrangement if their lower limits are under the cedents surplus retention amount?

Thanks a lot

 

Hi again,

The max under the surplus line is right.

The maximum EML covered by the surplus cover is, (k+1)*R.

Here it is, (4+1)*500 = 2500.

The key thing to remember with surplus lines cover is that it covers amounts proportional to the (k+1)*R bit, and not the actual loss, when working out the proportions.

In this example the eml is 2,300. Since they say that the insurer keeps the maximum retention, we set

(k+1)*500 = 2,300

then this means here k = 3.6, since this is less than 4.

The loss is proportionally split 1:k, 1:3.6, or 21.74% for the insured. If they want to take 3.6 lines, they could take less or more.

Now even if the loss is 100 billion it is still only the first 21.74% kept the insured. (Although, the reinsurers won't like this and will question why the eml is so low etc and might not pay)

So, the loss is actually 3500, so the insured keeps hold of 761.

So, the key is the proportional bit is to the (k+1)*r bit and the actual claim amount.

To the second point, xl contracts can be net or gross of all previous contracts in the real world. I think more often than not they will be based on the gross amount. This makes it easier to design an ri programme also. Imagine having to keep working out net amounts, then applying a new layer, then new net amounts etc.

They don't even have too be net of each other sometimes.... I know of one london market insurer who has two sets of recoveries made on the same 05 hurricane losses, so the net position gets a lot better when the gross goes up.

The xl layer could be placed where ever and it could cover most of the net loss after the surplus cover also. But the lower down the attachment point is, i.e. the more working layer it is, the more expensive it will be.

 

thanks again

These answers are very helpful Fiend. I really appreciate the time you've taken to explain them - thanks again.

Leala

 

Some further explanation required...

Hi Fiend

I've been doing some practice re the surplus type questions and I've come across one that's causing me problems, especially going about the question the way you explained below:

This is Sept 2001, Q5(iii)

The amount of the claim left after the first XL treaty is 4m. This is fine. So now I'm going to apply the surplus cover to this.

Since the insurer always cedes the minimum, this means he retains the maximum. He retains 3m and so the proportion of the EML he's retaining is 30%, and he cedes 70%. Thus every claim will be divided in these proportions (or 1:2.33).

70% of the net claim of 4m is 2.8m though.The solution says that B pays 2/5's of 4m.....so looks like my understanding isnt yet perfect.

Can you help me out on this one - thanks a lot

Leala

 

eeekkk you are doing past papers at this time and ones so far back. You must really want to nail this exam!

OK, you are close with your answer but it comes back to what the EML is. Here it is $10m gross of all reinsurance.

Since the surplus acts after the xl layer, the EML of $10m net of the xl layer is $5m.

If the cedant wants to cede the least, he will retain the maximum, so we set

(k+1)3 = 5, then we get k = 2/3 ... i.e. it is split 1:k, 60% and 40% and you get the answer 2/5 (40%) of 4m ceded.

 

Hi Fiend

Thanks again, oh if i was only as prepared as you think I am! This is a random past paper in the revision booklets, if i had done every question back as far as this, i dont think i'd be asking these questions. Never knew that about the 'net of the EML' thing, so thanks ever so much again.

Best of luck tomorrow!

Leala