SP2 September 2015, question 2(iii)

[Eleanor Cawston]

Hi,
I don't understand the calculation of the reinsurance premium for Treaty 2 in the examiner's report or the revision note booklets.
I understand these elements:
50,000 = 50% sum assured
1.1 = profit loading of 10%

But why is the assurance factor 2 x 0.057 when the question states that the reinsurer's risk premium rates are based on the insurer's original pricing? The original pricing had an assurance factor of 0.11.

A more general question: in the syllabus, the section on Reinsurance mentions describing the purpose / types / structures of reinsurance and factors to consider before taking it out. In particular, there is no mention of calculating anything, so is this no longer relevant to the syllabus? Or are pricing calculations still examinable as this is covered in earlier subjects so assumed knowledge?

Thanks,
Eleanor

 

[Mark Willder]

Hi,
I don't understand the calculation of the reinsurance premium for Treaty 2 in the examiner's report or the revision note booklets.
I understand these elements:
50,000 = 50% sum assured
1.1 = profit loading of 10%

But why is the assurance factor 2 x 0.057 when the question states that the reinsurer's risk premium rates are based on the insurer's original pricing? The original pricing had an assurance factor of 0.11.

A more general question: in the syllabus, the section on Reinsurance mentions describing the purpose / types / structures of reinsurance and factors to consider before taking it out. In particular, there is no mention of calculating anything, so is this no longer relevant to the syllabus? Or are pricing calculations still examinable as this is covered in earlier subjects so assumed knowledge?

Thanks,
Eleanor

Hi Eleanor

The syllabus also says "Demonstrate the application of reinsurance as a risk management technique", so I think doing numerical questions would be a good way of demonstrating how reinsurance works. So I think a numerical question on reinsurance is still possible on the current syllabus.

This was an incredibly difficult question. I'm afraid it's taken me a while to dig out an old ASET and find the time on a non-teaching day to make sure I understand it.

The ASET advice for Q2(iii) treaty B runs to 2 pages. In short it says that it is unlikely that anyone would have time to crunch out all the required algebra. It gives the general advice for numerical questions to do something practical, get as many method marks as you can in the given time, and then move on to the next question. It would be very easy on a question like this to waste half an hour scoring maybe one extra mark.

Looking at the calculation in detail, then yes you are right about the 50% sum assured and the 10% profit loading.

I agree that at first sight it looks odd that we are using the new pricing assumptions in the factor 0.057 when we should be using the original pricing basis of 0.11. But it is correct. We need to consider the probability that the reinsurance premium is paid and this will be on the new corrected mortality basis t_p_x. But you're right that the reinsurance premium itself is calculated on the old basis, ie twice the new corrected basis 2 * q_x. Multiplying the probability of payment by the reinsurance premium and discounting back gives us 2 * v^t * t_p_x * q_x all calculated on the new corrected basis. Summing each year's reinsurance premiums up then gives us twice the 0.057 factor as required.

I hope that helps to explain what is happening here. It's unlikely that a question exactly like this will come up again, but the general advice stands that if any unusual numerical question comes up, don't worry about getting it exactly right, but just do what you can in the time available for that question part.

Best wishes

Mark

 

[Eleanor Cawston]

Honestly, I'm not certain if that is comforting or not! Thanks for the details (and spending time digging them out - I did look at your answer at the time!).