April 2008, Q4

[Geraldine]

In the revision booklet, to get the annual amount we pay for the option using the North American method, the solution shows to divide by a select annuity factor, a[x]

I don't understand this because:

- Earlier in the solution we applied an annuity factor, ax, to the premiums paid prior to the option date
- We seem to have differentiated the mortality and morbidity experienced after the option date by using p'x and q'x (as opposed to px and qx)

So my understanding was that, ESSENTIALLY, ax was already a sort of select annuity factor. In other words, ax and associated px and qx are ALREADY select compared to the p'x and q'x and a'x+10 at the option date. So what exactly would a[x] mean?

(I do however agree with using a[x] in the conventional method as it seems to be consistent with the rest of the solution)

Hoping someone could help clarify this for me

 

[Sarah Byrne]

Hi Geraldine

You are quite right. The a[x] in the final step is not consistent with the rest of the solution. As you say, there is already selection allowed for in this situation via the death/CI rates used. This should be a(due)x:10 as used earlier in the solution.

We'll get the solution amended. Thanks for asking about this and apologies for the confusion it has caused you.

Good luck for the exam
Sarah