Cost of mortality option

[Minal Gohil]

Hello,

Can you please clarify the solution to question 23.4 in Ch#24, in particular, the calculation for total value of benefits on page 27 of the solution?

In my opinion, the total value of the benefit should be equal to the sum of -
A. The benefits under the two year term assurance product valued at AM92 ultimate mortality with a SA of 50,000
B. The additional benefit of 25,000 for one year for lives aged 51 who exercise the option (i.e. valued at 200% AM92 Ultimate)

Can you please illustrate how the equation of total value of benefits have been arrived at?

Regards,
Minal

 

[Mark Willder]

Hello,

Can you please clarify the solution to question 23.4 in Ch#24, in particular, the calculation for total value of benefits on page 27 of the solution?

In my opinion, the total value of the benefit should be equal to the sum of -
A. The benefits under the two year term assurance product valued at AM92 ultimate mortality with a SA of 50,000
B. The additional benefit of 25,000 for one year for lives aged 51 who exercise the option (i.e. valued at 200% AM92 Ultimate)

Can you please illustrate how the equation of total value of benefits have been arrived at?

Regards,
Minal

Hi Minal

You've asked an interesting question here as it demonstrates that the question is using a simplified approach to make the calculations easier than they would be in practice.

I'm afraid the method you quote doesn't fit the assumptions we've been told to use. We assume that the people taking up the option have 200% Ultimate mortality - importantly this applies to both their original benefit of 50,000 and the extra benefit of 25,000.

So the total value of the benefit should be equal to the sum of -
A. The benefits under the two year term assurance product valued at AM92 ultimate mortality with a SA of 50,000 for the 70% of lives that do not take up the option
B. For the 30% who do take up the option, the benefit of 50,000 for one year for lives aged 50 at 100% AM92 Ultimate and the benefit of 75,000 for one year for lives aged 51 valued at 200% AM92 Ultimate.

I agree that this is a rather strange assumption to make as the 200% mortality affects both the standard policy and the option. However, it is the assumption that the examiners have used at various times in the past. The main reason for using this approach is that it's a lot simpler than using the alternative approach that follows.

An alternative, more accurate, approach would be to assume that the lives were on average ultimate. So if the option takers were 200%, then the non-takers would be something like 50%, so the average would be around 100% (I haven't worked this out accurately, but it's close enough to give an indication of what we'd do). As you can see, this would make the calculation even harder, and so it's rarely been done in the exam.

I hope this helps to explain what we've done in the solution and why.

Best wishes

Mark

 

[Pulkit Agarwal]

Hi Minal

You've asked an interesting question here as it demonstrates that the question is using a simplified approach to make the calculations easier than they would be in practice.

I'm afraid the method you quote doesn't fit the assumptions we've been told to use. We assume that the people taking up the option have 200% Ultimate mortality - importantly this applies to both their original benefit of 50,000 and the extra benefit of 25,000.

So the total value of the benefit should be equal to the sum of -
A. The benefits under the two year term assurance product valued at AM92 ultimate mortality with a SA of 50,000 for the 70% of lives that do not take up the option
B. For the 30% who do take up the option, the benefit of 50,000 for one year for lives aged 50 at 100% AM92 Ultimate and the benefit of 75,000 for one year for lives aged 51 valued at 200% AM92 Ultimate.

I agree that this is a rather strange assumption to make as the 200% mortality affects both the standard policy and the option. However, it is the assumption that the examiners have used at various times in the past. The main reason for using this approach is that it's a lot simpler than using the alternative approach that follows.

An alternative, more accurate, approach would be to assume that the lives were on average ultimate. So if the option takers were 200%, then the non-takers would be something like 50%, so the average would be around 100% (I haven't worked this out accurately, but it's close enough to give an indication of what we'd do). As you can see, this would make the calculation even harder, and so it's rarely been done in the exam.

I hope this helps to explain what we've done in the solution and why.

Best wishes

Mark

Hi Mark,

Could you please explain why premium at the start of second year is calculated using AM92 Ultimate mortality?

Also, I would imagine that the current value of additional premium would be:
(1)PV of total benefits for all policies (who took and didn't took the option) - (2)PV of total benefits (assuming there is no option available)

Both (1) and (2) are calculated in the solution of this question. Therefore, the extra premium will be: 312.98-239.563 = 73.417.

Regards,
Pulkit

 

[Mark Willder]

Hi Mark,

Could you please explain why premium at the start of second year is calculated using AM92 Ultimate mortality?

Also, I would imagine that the current value of additional premium would be:
(1)PV of total benefits for all policies (who took and didn't took the option) - (2)PV of total benefits (assuming there is no option available)

Both (1) and (2) are calculated in the solution of this question. Therefore, the extra premium will be: 312.98-239.563 = 73.417.

Regards,
Pulkit

Hi Pulkit

The question tells us that premiums are calculated using ultimate mortality, so that is what we have done. I guess you were expecting the premium to be calculated using select mortality - most questions do use select mortality for the premiums to reflect the impact of the initial underwriting. However, in this question the insurer has decided that ultimate mortality better reflects its target market. Maybe this insurer doesn't do as much underwriting as the insurers that contributed to the standard select table.

I'm afraid your suggested calculation doesn't work. The option premium needs to cover the difference between all the benefits paid out (312.98) and all the standard premiums received (257.92). Your calculation has ignored the fact that by taking up the option, the policyholders have to pay additional standard premiums of 65.63.

Best wishes

Mark

 

[MindFull]

Hi Mark,

With regards to your above reply, I was actually expecting the premium to be calculated using the 200% since the option holders are now assumed to have higher mortality. The total value of the benefits takes into account the higher mortality when calculating the PV of $75,000. I just wanted to verify that the premiums indeed use the standard mortality that all phs are expected to have (including the 70%).

Regards.

 

[Mark Willder]

Hi Mark,

With regards to your above reply, I was actually expecting the premium to be calculated using the 200% since the option holders are now assumed to have higher mortality. The total value of the benefits takes into account the higher mortality when calculating the PV of $75,000. I just wanted to verify that the premiums indeed use the standard mortality that all phs are expected to have (including the 70%).

Regards.

A contract with a mortality option guarantees that the policyholder can exercise the option and pay just the standard premium rate for that contract. The insurer guarantees that the policyholder is accepted without any evidence of health, but is still going to pay standard rates (in this case standard rates are calculated using ultimate mortality, in most questions we are told to use select mortality). When a policyholder exercises the option, the insurer won't know whether they are healthy or not, but it must charge standard rates as promised.

This is a valuable option to the policyholder. So the insurer charges an extra premium on the original contract to cover the option cost. To do this it assumes that the option takers have high mortality (in this case 200%) when valuing the benefits.

So the trick is to use two sets of assumptions. Assume the high mortality when valuing the benefits, but the standard mortality when calculating the standard premium. The cost of the option (the extra premium) is then the difference between the expected present value of the benefits less the expected present value of the premium.

Best wishes

Mark