Alterations to Contracts

[Chan2009]

Can someone please answer my following queries

1) I dont understand the principle which is shown below met by the method "Paid-up value plus premium for balance of sum assured" is that

"If the paid-value is based on the surrender value i.e it is the latter thrown into reversion using the surrender value basis assumptions, then a reduction in the o/s term to zero would produce a normal surrender value.....""

An example would help here

2) I cannot get my head round that under the method "Equation of policy values", no profit would not emerge after the date of alteration if a realistic prospective value was used after the policy alteration.


Many Thanks

 

[Lynn Birchall]

Hi

1. Very roughly, the method being used here is:

1. Work out the paid-up SA on the original policy (as the policyholder is now "stopping paying premiums on the original policy").
2. Subtract this SA from the "new SA" the policyholder wants after the alteration.
3. The new premium the policyholder should pay is the normal premium that would be charged for this SA (ie for the gap between "new SA" and paid-up SA on the original).

(Step 2 is complicated by the fact that we need to apply assurance factors to the sums assured, rather than just subtract them, if the policy term is being altered.)

A general principle of a good alteration method is that if the alteration is "reduce the outstanding policy term", then the terms for the alteration look sensible when compared with the SV (which is the limiting case ie reducing the outstanding term to 0).

The bullet point you refer to is trying to say that, if we do steps 1 and 2 of the method on the same basis as we calculate SVs, then this principle will be met. If we use some other approach to calculate the paid-up SA, the principle may not be met. For example, if the PUP terms are a lot less generous than the SV terms and a policyholder shortens the outstanding term so that they pay just 1 more premium, they may find that, even with that one extra premium the benefit they get in one year is less than the SV they could have been paid immediately.

(Sorry that ended-up being slightly long-winded Hope it helps!)


2. Imagine you were pricing a new policy. If you did this using realistic assumptions, you would set premiums that you expected to be enough to cover benefits and expenses. You wouldn't expect to make any profit.

It's exactly the same result if we use realistic assumptions for a policy post-alteration. (Phew, that was shorter! )

Best wishes
Lynn

 

[Chan2009]

Hi

1. Very roughly, the method being used here is:

1. Work out the paid-up SA on the original policy (as the policyholder is now "stopping paying premiums on the original policy").
2. Subtract this SA from the "new SA" the policyholder wants after the alteration.
3. The new premium the policyholder should pay is the normal premium that would be charged for this SA (ie for the gap between "new SA" and paid-up SA on the original).

(Step 2 is complicated by the fact that we need to apply assurance factors to the sums assured, rather than just subtract them, if the policy term is being altered.)

A general principle of a good alteration method is that if the alteration is "reduce the outstanding policy term", then the terms for the alteration look sensible when compared with the SV (which is the limiting case ie reducing the outstanding term to 0).

The bullet point you refer to is trying to say that, if we do steps 1 and 2 of the method on the same basis as we calculate SVs, then this principle will be met. If we use some other approach to calculate the paid-up SA, the principle may not be met. For example, if the PUP terms are a lot less generous than the SV terms and a policyholder shortens the outstanding term so that they pay just 1 more premium, they may find that, even with that one extra premium the benefit they get in one year is less than the SV they could have been paid immediately.

(Sorry that ended-up being slightly long-winded Hope it helps!)

Many thanks for the reply

I tried to understand the above reply to my first query by using a following example:

Suppose that we have a 25 year NP EA (non-profit endowment assurance) and the altersation occurs at t=10. If we ignore the alteration expense and assume base the PUSA on the surrender values.

V(10) = S*A(x+10:15) +e*a(x+10:15) - P*a(x+10:15)

V(10) based on the paid-up policy is PUSA*A(x+10:15) +e*a(x+10:15)

(x:n-t) means policholder aged x and n-t is the o/s term of the policy
V(t) means the reserve at time t

Hence the notional PUSA is {V(10) - e*a(x+10:15)}/(A(x+10:15)}

Therefore the PUSA after the change is notional PUSA x {A(x+10:0)/A(x+10:15} which gives V(10) - e *a(x+10:15) hence not equal to the normal surrender value.

Looks like that I that I have misunderstood something. Please explain?

 

[Lynn Birchall]

Hello

Actually, I think your understanding looks fine, it's the method (and the simplified description of it) that's the problem!

What you've said is correct. The "throwing into reversion" using a ratio of assurance factors, which is what the Core Reading does when it first describes the method, is making an implicit assumption that expense differences can be ignored I think. This might not be too bad an assumption if the alteration in term is relatively small and keeps the method simple (this method is technically less good than "equating policy values" which is the best alteration method).

But, to do the limiting case of a reduction in term to 0 properly, the change in term would need to be reflected in the expenses as well as the benefits. So, in your example, the PUSA after the change would be worked out from:

{PUPSA A(x+10:0)} = {notional PUSA A(x+10:15)} + e *a(x+10:15)

(So, that when you substitute in the notional PUPSA this is equal to the normal surrender value.)

Sorry for any confusion caused. Hope this helps
Lynn

 

[Chan2009]

This is great. Many thanks for your help Lynn.