Chapter 24 - Cost of Guarantees&Options

[Avviey]

Hi,

I have quite afew questions about this chapter, can anyone kindly have a look?

1) Question 24.3, part ii) the insurance company protect itself from the annuity rate guarantee by purchasing interest rate swap options.

I understand "receive fixed/pay floating" swaps, but the answer says," the fix rate in the swap agreement was equal to the interest rate in the guaranteed annuity basis." What is this interest rate in guaranteed annuity basis? Is it the guaranteed annuity rate??


2)Question 24.4, the insurance company has instead invested to match the future annuity option and holds bonds.

What is this future annuity option which requires the company to hold bond put option as it opposed to open market cash option in Question 24.1? I think a guaranteed annuity rate corresponds to a call option on the bonds.


3) Under mortality option on page 12, it says, "In general, the smaller the proportion who exercise the option, the worse it 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." I would think the smaller, the better?


4)Question 24.15. the equation of EPV (outgo), the 30% of all policyholders survive to take up the option part, ....+30% * 100,000*(primed Endowment Assurance factor of 5 years' term + primed term assurance factor of 5 years' term).

So my question is shouldnt the sum assured be 200,000 rather than 100,000, as the 30% taking up the option of increasing sum assured to 200,000?

Secondly, why does it incude the primed term assurance factor in the equation? As I think the Endownment assurance factor has included the term assurance part.


I'd appreciate alot if anyone can help to clearify.

 

[Lynn Birchall]

Hi

Can I have a go at 1 to 3 now, and I'll have a look at 4 soon (if nobody posts in the mean-time!)

1) Question 24.3, part ii) the insurance company protect itself from the annuity rate guarantee by purchasing interest rate swap options.

I understand "receive fixed/pay floating" swaps, but the answer says," the fix rate in the swap agreement was equal to the interest rate in the guaranteed annuity basis." What is this interest rate in guaranteed annuity basis? Is it the guaranteed annuity rate??

Yes - it's the interest rate the company used to work out the guaranteed annuity rate.

2)Question 24.4, the insurance company has instead invested to match the future annuity option and holds bonds.

What is this future annuity option which requires the company to hold bond put option as it opposed to open market cash option in Question 24.1? I think a guaranteed annuity rate corresponds to a call option on the bonds.

Having given the guarantee, the company has a choice between 2 basic investment strategies:
(1) Invest in assets to provide the cash lump sum (and run the risk that the annuity option turns out to be more valuable to the policyholder, which will happen if interest rates are low at their retirement date)
(2) Invest in bonds to match the annuity payments (and run the risk that the cash lump sum option turns out to be the more valuable to the policyholder, which will happen if interest rates are high at their retirement date).

If the company has gone for strategy (1), then a call option on the bonds is a good idea - this is the situation in Question 24.3
If the company has gone for strategy (2), then a put option on the bonds is what's needed - this is the situation in Question 24.4

3) Under mortality option on page 12, it says, "In general, the smaller the proportion who exercise the option, the worse it 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." I would think the smaller, the better?

I think it's correct as it is. The idea is that if take up of the option is low, it's likely to be those policyholders with most to gain who will have taken up the option (ie those with the worst expected mortality experience). If a big proportion of eligible policyholders have exercised the option, there are likely to be more "normal" mortality policyholders included in the group who have exercised.

Best wishes
Lynn

 

[Avviey]

Hi Lynn,

Many thanks for Q1 and Q3. Just a couple of points about Q2 that I'm still not sure about.

Having given the guarantee, the company has a choice between 2 basic investment strategies:

(1) Invest in assets to provide the cash lump sum (and run the risk that the annuity option turns out to be more valuable to the policyholder, which will happen if interest rates are low at their retirement date)

1)/a) The cash lumpsum is the maturity payment from Endowment Assurance?

1)/b) By looking back at Q 24.1, the answer says,' the company is at risk from low interest rates since the annuity may cost more to buy than the cash available.' Why does the company need to buy the annuity? Shouldnt it be the policyholder who buys the annuity? Why does annuity option become more valuable if interest rates drop?

I think I'm confused about the whole Q24.1, Q24.3 and Q24.4 and the links in between.

(2) Invest in bonds to match the annuity payments (and run the risk that the cash lump sum option turns out to be the more valuable to the policyholder, which will happen if interest rates are high at their retirement date).

The annuity payments here mean regular annuity payments from the deferred annuity contact?

Heaps of thanks again.

 

[Avviey]

Hi, Just wonder if anyone get the chance to take a look at this?

Many thanks.

 

[fischer]

1)/a) - Yes, I think that's correct.

1)/b) - AT THE TIME OF TAKING OUT THE CONTRACT the company has given the PH a guarantee that the PH can use the mat proceeds (say £200,000) to buy an annuity (£10,000 pa say).
The company has calculated this assuming interest = 5%, i.e. 200,000*5% = 10,000 (and mortality = 0 )
So, the company has to buy the annuity for the PH on guaranteed terms if the PH exercises his option to do so.

Now if at mat, actual interest rates are 4%, AND
if the PH decides not to exercise his option but takes the £200,000 and goes to the market to buy an annuity, he will only get £8,000pa in exchange for the £200,000.

But the PH knows that the company has guaranteed £10,000 pa for the same £200,000. So, the PH will exercise the option as it has become more valuable.

(2) Not sure I've understood correctly what's going on here, but the converse of the above is true if the interest rates rise.
Now if at mat, actual interest rates are 8%, AND
if the PH decides to exercise his option he will give the company the £200,000 and the company in return will provide £10,000p.a.

As interest rates have risen the annuity that can be bought with the £200,000 is now £16,000pa.

This is exactly what the company will want. The company will invest in bonds that provide 8% return. Each year the company will receive £16,000pa. It will pay the PH the guaranteed £10,000pa and keep the remaining £6,000 pa



if the PH decides to go to the market and buy an annuity, he/she will receive £16,000. So, the PH will be better off to take the cash lumpsum instead.

Hope this helps.

Good luck.

 

[TheProtea]

4)Question 24.15. the equation of EPV (outgo), the 30% of all policyholders survive to take up the option part, ....+30% * 100,000*(primed Endowment Assurance factor of 5 years' term + primed term assurance factor of 5 years' term).

So my question is shouldnt the sum assured be 200,000 rather than 100,000, as the 30% taking up the option of increasing sum assured to 200,000?

Secondly, why does it incude the primed term assurance factor in the equation? As I think the Endownment assurance factor has included the term assurance part.

If you still interested in this Q4,
The first part of question, I think is correct as is in the solution. Only the death benefit is increased by 100,000 to 200,000 on taking the option. So you can think of this benefit (after exercising) as 100,000 Endownment+100,000 Term policies (as the notes do). Or see it as just 100,000 "Pure Endownment"+200,000 Term policies.
The main point is that if the PH who exercised the option dies they would get 200,000, else if they survive to maturity they would get only 100,000 (as it is not part of the option).
I guess this also answer the 2nd part.
Cheers

 

[Avviey]

Thank you to you both. All clear now.