Incidence rate Vs Inception rate

Hi Vatsal

I'll answer your questions in turn:

Q1 - The terms 'claims incidence' and 'claim inception' are often used used interchangeably to mean the claim rate. However, it is more accurate to use claims incidence to refer to single events that lead to a lump sum payment (eg critical illness lumps sums or PMI), and to use claims inception for claims that have a start and end point and so lead to regular payments (eg income protection or long-term care) so we have the claim incepting and then at a later date the claim terminating (eg on death or recovery).

Q2 - The Core Reading is correct.

We could use all three methods using a cashflow approach, ie we do a profit test by projecting the future profits (premiums plus investment return less claims less expenses plus release of reserves) and then discounting them back at the risk discount rate. We can make these calculations more prudent by adding margins to assumptions (eg assuming IP policyholders are sick for longer) or by using a higher risk discount rate (which places a lower value on the profits).

Alternatively we can price using a formula. This is similar to the life insurance calculations you will have seen in CM1, eg an annuity is valued using the little a function. The yellow tables include similar annuity functions for income protection on page 139, although using these functions was removed from the syllabus a few years ago. We can use method 1 to add a margin to these formulae by assuming people remain in sickness for longer or using a lower rate of interest when calculating the little a functions.

Note that there is no risk discount rate in the formula approach so we can't use it to add prudence to the formula calculation. Also note that adding prudence for the cashflow approach means a higher risk discount rate (the rate used to discount profits), while adding a margin to the investment assumption (the return earned on the cashflows) means using a lower interest rate.

I hope these explanations help.

Best wishes

Mark