C23 Cost of guarantees and options

Question 1

Give three examples of investment guarantees offered by savings products

Answer 1

Investment guarantees

1. Guaranteed minimum maturity value
2. Guaranteed minimum surrender value
3. Guaranteed annuity option

Question 2

Discuss the investment risk faced by a life company when it offers guarantees

Answer 2

Investment risk faced by life company offering guarantees

 Risk assumed by life company is that at specified times in future, ‘backing’ assets will be insufficient to meet guarantees.
 If company has control over investment policy, eg traditional contracts with guarantees, then there is conflict between investing to meet guarantees and investing for maximum performance.
 If company chooses not to invest to match guarantees, it must include cost of guarantee in original pricing basis.
 If company has no control over investment policy, eg unit-linked endowment assurance, the guarantee’s cost must be included in original charges to the extent that the guarantee won’t be matched.

Question 3

Describe what is meant by the liability created by an investment guarantee

Answer 3

Liability created by investment guarantee

 = Guaranteed amount – Cost that would have been incurred in absence of guarantee

 Here guaranteed amount is:
– guaranteed maturity value of endowment, or
– guaranteed surrender value, or
– fund needed to purchase ‘guaranteed annuity’ at current market rates.

 Policyholder should only choose to exercise option to take up this
guarantee if it is ‘in-the-money’, ie financially advantageous.

Question 4

Outline the two main ways in which the extra premium or charges needed to cover the cost of an investment guarantee can be assessed.

Answer 4

Two ways to assess extra premium/charges needed to cover cost of guarantees

1. Option-pricing/market valuation techniques
   – Assess extra premium/charges by looking at market price of derivative that insurer could acquire to mitigate its risk.
2. Stochastic simulation of investment performance
   – Extra sums likely to be needed under guarantee can be modelled by simulating range of investment scenarios.

Question 5

State the type of option to which each of the following guarantees corresponds:
 guaranteed minimum maturity value
 guaranteed minimum surrender value
 guaranteed annuity rate.

Answer 5

Guarantees in terms of options

 Guaranteed minimum maturity value – corresponds to (European-style) put option on investment funds at exercise price corresponding to maturity guarantee.
 Guaranteed minimum surrender value – corresponds to similar American-style option, or series of options with different exercise prices that match guaranteed surrender values.
 Guaranteed annuity rate – corresponds to call option on bonds that would be necessary to ensure guarantee was met, ie at exercise price that generated required fixed rate of return.

Alternatively, can be mirrored by option to swap floating rate returns at
option date for fixed rate returns sufficient to meet guaranteed annuity
option (using swaption).

Question 6

Explain what is meant by stochastic simulation in the context of assessing the
cost of guarantees.

Answer 6

Stochastic simulation – assessing cost of guarantees
 By projecting forward value of assets using a stochastic investment model and comparing this with sum payable under guarantee, insurance company can measure extent to which additional costs will be incurred under range of investment scenarios.
 Stochastic model of rates of return on investments is used to simulate future price of assets.
 Assumptions underlying model chosen to correspond to company’s planned investment strategy.
 Large number of simulations needed to obtain reliable estimates.
 If liability depends on future market conditions (eg guaranteed annuity rates), then factors influencing value of liabilities also need to be simulated.

Question 7

Explain how stochastic simulation is used to estimate a premium to cover the
cost of a financial option.

Answer 7

Use of stochastic simulation to estimate premium to cover cost of option

 Need assumptions about future rates of exercising options, taking into account:
– expected policyholder behaviour
– size of guaranteed amount relative to the alternative benefit, eg asset share.
 Determine present value of liability, by discounting simulated cost of exercising option at suitable rate.
 Carry out many simulations to generate probability distribution of present value of cost of option.
 Set premium so that its present value reflects the ‘market cost’ of providing the guarantee, eg the expected (average) simulated cost plus a margin.

Question 8

Give three examples of common life insurance policy mortality options.

Answer 8

Common life insurance policy mortality options
1. To purchase additional benefits without providing further evidence of health, at normal premium rates (for life of that age) at date on which option is exercised

2. To renew life insurance policy, eg term assurance, at end of its original term without providing additional evidence of health
3. To change part of sum assured from one contract to another, eg from term assurance to endowment assurance

Question 9

Describe how the terms and conditions under which an option can be exercised may be designed so as to reduce selection against the life company.

Answer 9

Terms and conditions under which an option can be exercised

 Often an option can be exercised only at fixed points of time, eg at end of every five years or at any time after a qualifying event has occurred, eg birth of child.

 Extent of option will also be specified, eg additional sum assured cannot exceed original sum assured.

Question 10

Describe the cost to the company of a life insurance policy mortality option

Answer 10

Cost of life insurance policy mortality option
 Equals value of excess of premium that should, with full underwriting, have been charged for additional assurance over normal premium rate actually charged.
 If life in good health and would satisfy normal underwriting requirements, then option generates little or no additional costs.
 If life in bad health, exercise of option generates considerable additional costs.
 Total expected additional costs depend on:
– health status of those who exercise option
– proportion of lives that choose to exercise option.

Question 11

Describe how a mortality option would be valued.

Answer 11

How to value a mortality option
 Cashflow projections would normally be used.
 Cashflows include additional benefits and premiums expected to be paid in relation to the option.
 Cashflows allow for the extent to which the option is assumed to be taken up.
 Additional premiums based on the expected premiums to be charged to standard lives, as at the option exercise date.
 Allow for additional expenses relating to option.
 For pricing purposes, allow for additional reserves to be held.

Question 12

List the five extra assumptions required to price a contract if a mortality option
is added.

Answer 12

Assumptions required to price a mortality option
1. Probability that option will be exercised, at each possible exercise date
2. Additional benefit that will be chosen, if at discretion of policyholder
3. Expected mortality of lives who choose to exercise option
4. Expected mortality of lives who choose not to exercise option
5. Additional expenses relating to option

Question 13

What are the two alternative assumptions that can be made regarding the option take-up rates?

Answer 13

Option take-up rate assumption

1. Assume that all eligible policyholders will take up the option, and that the maximum additional benefit will always be taken.
   If there are several alternative options or exercise dates, the model may assume that the worst option from the financial point of view of the company is chosen with probability one.
2. Assume more sophisticated take-up rates which vary by exercise date or by alternative option. These would ideally be based on past experience.

Question 14

What are the two alternative assumptions that are typically made regarding the mortality of those lives that don’t take up a mortality option?

Answer 14

Assumed mortality if don’t take up mortality option
1. Assume lives that don’t take up option will continue to experience base mortality.
Implies that average mortality for all lives is higher than the base mortality assumption (because those taking up the option assumed to experience higher than base mortality).
2. Assume that mortality of those who don’t take up option is such that average mortality for all lives remains at the expected base level.
Here, assumed mortality of those who do not take up the option would
be less than for (1), ie less than base mortality.

The insurer may instead assume that everyone exercises the option.