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Chapter 23

K

kimiko

Very Active Member
On page 14, it says "In general, the smaller the proportion who exercise the option, the worse will be the subsequent mortality experience of those exercising the option. If a substantial proportion exercise the option, then their subsequent mortality experience will on average be less extreme." but in the solution to the question it says "The first is worst – if everyone with higher than select mortality takes up the option.". From what I understand, the former is referring to a substantial proportion of the total portfolio.

However, then below that it says "The encouragement given to policyholders to exercise the option. As discussed in the Core Reading, if take up of the option is low it tends to be only those who have most to gain who exercise the option. As explained in the previous question, this can be a good thing, as it could keep the total cost of the option low." Shouldn't we want more policyholders to exercise the option from the Core Reading (ie former sentence)?

Secondly, the formula given on the same page: "So the cost of a mortality option is (roughly speaking) the product: {proportion of lives exercising option}x{average health of lives exercising option}" Shouldn't it be the inverse of this formula? So higher proportion would make the cost lower from the former Core Reading sentence and average health higher would make the cost lower as well?

Not sure if my understanding is correct for this.
 
Thirdly, can you kindly explain this from page 17 "It may instead be assumed that the mortality experience of those who take up the option will be the Ultimate experience which corresponds to the Select experience that would have been used as a basis if underwriting had been completed as normal when the option was exercised."?

Doesn't this lead to a lower mortality since Select experience is lower or does this mean the Ultimate experience will be used ie what the policyholders' mortality rate would have been even without the option take up?

I think I am confused because after that it says this: "However, this would mean that the average mortality for all lives has been assumed to be more than the base mortality assumption, since those taking up the option are assumed to experience higher mortality than this level." which makes me think that the sentence previously means that the mortality rate assumed is higher than the base (ie Ultimate) which is not what I understand.
 
Last edited:
kimiko said:
On page 14, it says "In general, the smaller the proportion who exercise the option, the worse will be the subsequent mortality experience of those exercising the option. If a substantial proportion exercise the option, then their subsequent mortality experience will on average be less extreme." but in the solution to the question it says "The first is worst – if everyone with higher than select mortality takes up the option.". From what I understand, the former is referring to a substantial proportion of the total portfolio.

However, then below that it says "The encouragement given to policyholders to exercise the option. As discussed in the Core Reading, if take up of the option is low it tends to be only those who have most to gain who exercise the option. As explained in the previous question, this can be a good thing, as it could keep the total cost of the option low." Shouldn't we want more policyholders to exercise the option from the Core Reading (ie former sentence)?

Secondly, the formula given on the same page: "So the cost of a mortality option is (roughly speaking) the product: {proportion of lives exercising option}x{average health of lives exercising option}" Shouldn't it be the inverse of this formula? So higher proportion would make the cost lower from the former Core Reading sentence and average health higher would make the cost lower as well?

Not sure if my understanding is correct for this.
Click to expand...
Hi Kimiko

A numerical example might help.

If only 10 people exercise the option then it is likely that they will have very poor health, ie there is a lot of anti-selection. So the cost per policy might be 100 and the total cost is 10 x 100 = 1000.

However if in addition to the 10 very unhealthy live mentioned above, we also have another 100 policyholders exercise the option. It is likely that these have only moderately poor health and so might have average cost of 20. So the total cost is 10 x 100 + 100 x 20 = 3,000.

So we can see that it is worse if lots of lives exercise the option, despite the average cost being lower.

Best wishes

Mark
 
kimiko said:
On page 14, it says "In general, the smaller the proportion who exercise the option, the worse will be the subsequent mortality experience of those exercising the option. If a substantial proportion exercise the option, then their subsequent mortality experience will on average be less extreme." but in the solution to the question it says "The first is worst – if everyone with higher than select mortality takes up the option.". From what I understand, the former is referring to a substantial proportion of the total portfolio.

However, then below that it says "The encouragement given to policyholders to exercise the option. As discussed in the Core Reading, if take up of the option is low it tends to be only those who have most to gain who exercise the option. As explained in the previous question, this can be a good thing, as it could keep the total cost of the option low." Shouldn't we want more policyholders to exercise the option from the Core Reading (ie former sentence)?

Secondly, the formula given on the same page: "So the cost of a mortality option is (roughly speaking) the product: {proportion of lives exercising option}x{average health of lives exercising option}" Shouldn't it be the inverse of this formula? So higher proportion would make the cost lower from the former Core Reading sentence and average health higher would make the cost lower as well?

Not sure if my understanding is correct for this.
Click to expand...
Hi Kimiko

A numerical example might help.

If only 10 people exercise the option then it is likely that they will have very poor health, ie there is a lot of anti-selection. So the cost per policy might be 100 and the total cost is 10 x 100 = 1000.

However if in addition to the 10 very unhealthy live mentioned above, we also have another 100 policyholders exercise the option. It is likely that these have only moderately poor health and so might have average cost of 20. So the total cost is 10 x 100 + 100 x 20 = 3,000.

So we can see that it is worse if lots of lives exercise the option, despite the average cost being lower.

Best wishes

Mark
 
kimiko said:
On page 14, it says "In general, the smaller the proportion who exercise the option, the worse will be the subsequent mortality experience of those exercising the option. If a substantial proportion exercise the option, then their subsequent mortality experience will on average be less extreme." but in the solution to the question it says "The first is worst – if everyone with higher than select mortality takes up the option.". From what I understand, the former is referring to a substantial proportion of the total portfolio.

However, then below that it says "The encouragement given to policyholders to exercise the option. As discussed in the Core Reading, if take up of the option is low it tends to be only those who have most to gain who exercise the option. As explained in the previous question, this can be a good thing, as it could keep the total cost of the option low." Shouldn't we want more policyholders to exercise the option from the Core Reading (ie former sentence)?

Secondly, the formula given on the same page: "So the cost of a mortality option is (roughly speaking) the product: {proportion of lives exercising option}x{average health of lives exercising option}" Shouldn't it be the inverse of this formula? So higher proportion would make the cost lower from the former Core Reading sentence and average health higher would make the cost lower as well?

Not sure if my understanding is correct for this.
Click to expand...
Hi Kimiko

A numerical example might help.

If only 10 people exercise the option then it is likely that they will have very poor health, ie there is a lot of anti-selection. So the cost per policy might be 100 and the total cost is 10 x 100 = 1000.

However if in addition to the 10 very unhealthy live mentioned above, we also have another 100 policyholders exercise the option. It is likely that these have only moderately poor health and so might have average cost of 20. So the total cost is 10 x 100 + 100 x 20 = 3,000.

So we can see that it is worse if lots of lives exercise the option, despite the average cost being lower.

Best wishes

Mark
 
kimiko said:
On page 14, it says "In general, the smaller the proportion who exercise the option, the worse will be the subsequent mortality experience of those exercising the option. If a substantial proportion exercise the option, then their subsequent mortality experience will on average be less extreme." but in the solution to the question it says "The first is worst – if everyone with higher than select mortality takes up the option.". From what I understand, the former is referring to a substantial proportion of the total portfolio.

However, then below that it says "The encouragement given to policyholders to exercise the option. As discussed in the Core Reading, if take up of the option is low it tends to be only those who have most to gain who exercise the option. As explained in the previous question, this can be a good thing, as it could keep the total cost of the option low." Shouldn't we want more policyholders to exercise the option from the Core Reading (ie former sentence)?

Secondly, the formula given on the same page: "So the cost of a mortality option is (roughly speaking) the product: {proportion of lives exercising option}x{average health of lives exercising option}" Shouldn't it be the inverse of this formula? So higher proportion would make the cost lower from the former Core Reading sentence and average health higher would make the cost lower as well?

Not sure if my understanding is correct for this.
Click to expand...
Hi Kimiko

A numerical example might help.

If only 10 people exercise the option then it is likely that they will have very poor health, ie there is a lot of anti-selection. So the cost per policy might be 100 and the total cost is 10 x 100 = 1000.

However if in addition to the 10 very unhealthy live mentioned above, we also have another 100 policyholders exercise the option. It is likely that these have only moderately poor health and so might have average cost of 20. So the total cost is 10 x 100 + 100 x 20 = 3,000.

So we can see that it is worse if lots of lives exercise the option, despite the average cost being lower.

Best wishes

Mark
 
kimiko said:
Thirdly, can you kindly explain this from page 17 "It may instead be assumed that the mortality experience of those who take up the option will be the Ultimate experience which corresponds to the Select experience that would have been used as a basis if underwriting had been completed as normal when the option was exercised."?

Doesn't this lead to a lower mortality since Select experience is lower or does this mean the Ultimate experience will be used ie what the policyholders' mortality rate would have been even without the option take up?

I think I am confused because after that it says this: "However, this would mean that the average mortality for all lives has been assumed to be more than the base mortality assumption, since those taking up the option are assumed to experience higher mortality than this level." which makes me think that the sentence previously means that the mortality rate assumed is higher than the base (ie Ultimate) which is not what I understand.
Click to expand...
Hi Kimiko

In your first two paragraphs you are looking at the case where we assume 100% take up of the option assuming ultimate mortality. The standard premium will be based on select mortality in a particular table. We are just saying that we then price the option using the corresponding ultimate mortality from that table.

Your third paragraph is looking at a different case where we assume that a proportion take up the option and have worse than ultimate mortality and the non-takers have ultimate mortality.

Best wishes

Mark
 
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