per event XL treaty & aggregate deductible

[r_v.s]

This is a very elementary question, i suppose! But wold you please explain how an aggregate deductible works in a per event XL treaty (like the one in the last question in the sept 2008 paper)?

 

[Darren Michaels]

The aggregate deductible reduces the amount of recoveries that the insurer is able to recover from the reinsurance layer.

Amounts that would otherwise be recovered from the layer must erode the aggregate deductible first before any recoveries can be made from the layer.

Consider a risk XL layer of $1m xs $1m with an aggregate deductible of $2m. Suppose the insurer has 5 losses each of size $1.5m. The first 4 contribute $0.5m each to the aggregate deductible, so nothing in fact is actually recovered from the reinsurer. For the 5th loss, since the aggregate deductible is now fully eroded, $0.5m will be recovered from the reinsurer.

Have a look at SAQ 14.11 for more practice on deductibles.

 

[maz1987]

Let's say you have a number of losses, which contribute amounts A, B, C, ... to the layer.

If there is an aggregate deductible of X, then to calculate the recoveries using an Excel formula you would enter:

=Max(Sum(A,B,C,...)-X, 0)

(this assumes there is no aggregate limit)

In other words, sum the recoveries that would be made if there were no aggregate deductible, and then the cedant can only begin making recoveries once the sum of losses has exceeded the aggregate deductible, in which case they recover the amount excess of the aggregate deductible.

 

[r_v.s]

Thank you all very much! that was really helpful!