In part (B) of this question the cost of guarantee on maturity is calculated simply as the difference between the guaranteed amount and the fund value at the end. but shouldn't we also consider the probability of survival till the end i.e the probality of survival in the fifth year. So shouldn't we multiply the given value in the solutions with .998 ?
They have done it to find the profit per policy in force at inception to find the profit signature and further to find the NPV. It is not done to consider the survival till the end.
Hi This is a good question. As a caveat I haven't looked at the question you refer to. That said, strictly speaking my view is you may have a point. However, by convention the cost of guarantee is defined as max(0, guarantee - UF). Unit linked policies with guarantees will not only be the domain of life companies and in any case mortality will be less of an issue as the contract is a savings product. Thus ignoring it is likely to be immaterial. Non insurers offering unit linked policies with guarantees will almost certainly ignore mortality assumptions so in this regard ignoring it for insurers will be consistent. It is arguably more important to allow for withdrawal rates as this would have a bigger impact on the CoGs; I suspect withdrawal rates have been ignored in the question. Hope that helps. Hopefully it's sufficient to stop me needing to look at the question
Thanks a lot mugono, I got the answer. They have ignored the withdrawal rates. But, if we take mortality rates into consideration while finding the cost of guaranteed maturity it will not be considered wrong. Right?
My understanding says that we shouldn't include survival probability for the last year. Although it's given in the question that Death benefit = Fund value, but this thing doesn't apply to last year because he has paid full 5 premiums now. So he's entitled to receive MAX(fund value, guaranteed amount) at maturity date regardless of whether he survives last year or not. Also it's in the wording of part (b), that maturity value = MAX(fund value, guaranteed amount). So company must make a payment of MAX(fund value, guaranteed amount) at maturity date to him or his family regardless of whether he was alive at the end of year 5 or not. Hope this clears your doubt.
My advice would be to be consistent with the convention used and the examiner's approach. This is what will get you a pass in the exam. The key thing is to understand the principles in the course AND to pass the exam. There are no marks for being 'too clever'.
