Cost Of Guarantees And Options

Question 1

List examples of investment guarantees

Answer 1

1) Guaranteed minimum maturity values (for both unit-linked and non-linked endowment contracts)
2) Guaranteed minimum surrender values (for both unit-linked and non-linked endowment contracts)
3) The ability to convert a lumo sun into an annuity or vice versa on guaranteed terms

Question 2

What liability is created by an investment guarantee?

Answer 2

The excess of the guaranteed amount over the cost that would have been incurred at the time in the absence of a guarantee

Question 3

List the methods that may be used to determine the liability created

Answer 3

1) Option-pricing techniques
2) Stochastic simulation

Question 4

Option-pricing techniques to value liabilities created by investment guarantees

Answer 4

The value of the liabilities will be similar to the cost of a derivative which covers a similar guarantee or option to that which the company is offering. Only works if there exists a sufficiently close hedging asset to match the guarantee offered

Question 5

Stochastic simulation to value liabilities created by investment guarantees

Answer 5

The extra sums likely to be needed under the guarantee can be modelled stochastically by running a simulation of investment returns thousands of times

Question 6

List examples of mortality options

Answer 6

1) Extending the term without providing further evidence of health
2) Increasing the level of cover at normal premium rates without providing further evidence of health

Question 7

How may mortality options be valued?

Answer 7

Using a discounted cashflow model with assumptions for…

• option take-up rate
• benefit chosen
• mortality of those that exercise the option
• mortality of those that do not
• expenses relating to the option

Question 8

How may option take-up rates be set?

Answer 8

1)
- Assume all eligible policyholders take up the option
- Assume maximum benefit is always taken
- Assume the worst-case scenario from the insurer’s PoV

This method is simplistic but unlikely to be borne out in practice.

2)
- Assume a more sophisticated take-up rate
- These may vary by exercise rate or alternative options
- These are based on past experience

This method may be more realistic but it may be difficult to obtain the necessary data

Question 9

Cost of a mortality option =

Answer 9

= (proportion of lives exercising option).(average health of lives exercising option)

Question 10

List the factors affecting mortality options

Answer 10

SCENTE

Selective withdrawals
Conditions attaching to exercising the option
Encouragement given to policyholders to exercise the option
Number of times the policyholder gets the chance to exercise the option
Term of policy with the option
Extra cost to the policyholder who exercises the option

Question 11

How might the higher mortality of option-exercising individuals be incorporated into the model

Answer 11

1) A higher % of base mortality
2) An age loading may be applied
3) Ultimate mortality may be used for those who exercise the option while select is used for those who don’t