Chapter 27

Question 1

What are the different things that we should think of when determining the cost of options and guarantees?

Answer 1

• Reserving
• Product design
• Marketing
• Distribution channels
• Underwriting levels needed

Question 2

What risks do traditional life insurance contracts transfer to the insurance company?

Answer 2

• Mortality
• Expenses
• Investment

Question 3

What risk does investment-linked contracts leave with the PH?

Answer 3

Investment risk

Question 4

How can the attraction of investment-linked contracts be enhanced?

Answer 4

• If part of the investment risk is transferred to the IC
• A way of doing this is by offering investment guarantees, example:
  – Guaranteed min maturity values (UL and non-linked endowment contracts)
  – Guaranteed min SVs (both UL and non-linked contracts)
  – Ability to convert a lump sum into an annuity or vice versa on guaranteed terms

Question 5

Why do with-profits contracts transfer investment risk back to the PH to a lesser extent than for UL contracts?

Answer 5

• They typically have some level of guaranteed benefit - equivalent to an investment guarantee - e.g. basic SA plus attaching bonuses for conventional with-profits business under additions to benefit approach

Question 6

How can the attraction of traditional policies be enhanced?

Answer 6

If the IC provides guarantees of investment performance - e.g. an option can be provided to convert the maturity value of without-profits EA into an immediate annuity on guaranteed terms

Question 7

What is the main risk to the IC with regards to options and guarantees?

Answer 7

That at specified times in the future, the “backing” assets will be insufficient to meet the guarantees.
* Particularly difficult to control if the PH has a choice over whether to exercise the option
* If the guarantee relates to surrender, the IC will not know the specified time at which the assets must cover the liability
* The risk will also depend on the outstanding term of the policy:
– Longer time frame involved: greater chance that things might go wrong compared with current forecasts
– For conventional with-profits business a long time frame may give IC time to act on profit distribution levels in event of e.g. disappointing investment returns

Question 8

If an IC has control over the investment policy, e.g. traditional contracts with guarantees, what are the two sides of investing to meet policy benefits?

Answer 8

• There is conflict between investing to meet guarantees and investing for max performance
• If the LIC invests in assets backing a with-profit contract:
  – to meet the min guarantee, PHs will receive the min return and will miss out on the potential for any outperformance
  – to not match guarantees, company must include the cost of guarantee in the pricing basis

Question 9

If an IC has no control over the investment policy, e.g. UL EA, how should they allow for the cost of any guarantees?

Answer 9

They must include the cost of guarantee in the original charges to the extent that the guarantee will not be matched.

Question 10

What liability is created by an investment guarantee?

Answer 10

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

Question 11

Why should an IC be able to model an investment guarantee?

Answer 11

To quantify extra liabilities that will incur when the guaranteed amount exceeds the earned AS.

Question 12

When should a PH exercise a guarantee?

Answer 12

Only if it is financially advantageous to the PH - if the guarantee bites or it is in the money.

Question 13

True or False. An insurance company will seek to charge additional premium to meet liabilities created by the guarantee?

Answer 13

True.

Question 14

True or False. Whether the IC mismatches through choice or necessity, it will need extra funds from the increased premiums and charges to offset risk.

Answer 14

True.

Question 15

How can the liabilities created by options and guarantees be assessed?

Answer 15

• Option-pricing techniques
• Stochastic simulations

Question 16

How does option-pricing techniques work for valuing liabilities?

Answer 16

• They value liabilities by looking at market price of a derivative that the IC could acquire to mitigate its risk
• Options incorporated into LI contracts are analogous to options traded in the marketplace

Question 17

How can options be used to cost the minimum maturity value?

Answer 17

• The min maturity value corresponds to a European style put option on the investment funds at an exercise price corresponding to the maturity value

Question 18

How can options be used to cost the minimum SV?

Answer 18

• The min SV corresponds to an American style put option or a series of options with different exercise prices which match the guaranteed SVs
• The PH can exercise the option whenever they want to

Question 19

How can options be used to price a guaranteed annuity rate?

Answer 19

• Use a European style call option on the bonds that would be necessary to ensure the guarantee could be met, at an exercise price which generates the required fixed rate of return.
• European style put options on the IRs
• An option to receive a fixed IR sufficient to meet the guaranteed annuity option and pay the variable IR at the option date (“swaption”)

Question 20

If market prices are not available for the options used to cost financial guarantees or options …

Answer 20

estimates can be provided by market participants.

Question 21

What is the value of a guarantee at the date of the policy issue?

Answer 21

All guarantees are expected to be out of the money - will have no intrinsic value because current market rates are more than sufficient to meet guarantees. Will have a time value which is the result of views of the market of the PV of likely future costs.

Question 22

Is it possible for a guarantee to not be out of the money at date of policy issue?

Answer 22

Yes, but insurance companies might still offer these guarantees if they believe there is a very high chance of the guarantee being out of the money at the exercise date.

Question 23

How can stochastic simulations be used to cost a financial option or guarantee?

Answer 23

• By projecting forward the value of assets using a stochastic investment model and comparing this with the SA payable under a guarantee, the IC can measure the extent to which the additional costs will be incurred under a range of investment scenarios
• Assumptions underlying the model must be evaluated to ensure they correspond to the IC’s investment strategy
• Large number of simulations needed to obtain reliable estimates
• Key assumptions will be the PDF used to model the investment return and the mean and variance

Question 24

Describe the stochastic simulation method for pricing an annuity rate guarantee on a UL product.

Answer 24

1. Use a stochastic model of interest rates to project interest rates (bond yields) to those ages where the option could be exercised
2. Assess the probability of interest rates falling below the guaranteed rate and apply to projected fund values to estimate the potential cost
3. Calculate a discounted value of the potential cost

Question 25

Describe the stochastic simulation method for costing a min guaranteed maturity value for a UL policy.

Answer 25

1. Generate a sequence of random numbers 2. Use these to obtain a sequence of random N (0,1) variates 3. Use these to obtain a sequence of investment returns for the following m years 4. Use these to calculate the simulated accumulated fund (AF) 5. Compare this value with the guaranteed amount: * If the simulated fund is ≥ guaranteed amount: cost = 0 * If the simulated fund is < guaranteed amount: cost = guaranteed amount – AF 6. Repeat this process 10 000 times 7. Take the cost of the guarantee as the average cost over these 10 000 runs

Question 26

How would you cost the guaranteed SA under a without-profits policy using stochastic simulation?

Answer 26

You would use the similar approach for costing a min maturity value under a UL policy with the following differences: * Instead of simulating the accumulated fund value, simulate the AS of the policy for a certain premium and compare this with the SA. * The premium should then be varied until the probability and amount of loss are acceptable

Question 27

What is the disadvantage of using stochastic simulations to cost a guarantee?

Answer 27

It will only provide an estimate due to: * Model error * Parameter error * Random fluctuations

Question 28

What should an IC consider when making assumptions about the future rates of exercising options?

Answer 28

* Expected PH behaviour * Size of the guarantee relative to the alternative benefit

Question 29

How can an IC determine the PV of the liability created by a guarantee/ option using stochastic simulation?

Answer 29

Discount the simulated cost of exercising the option at a suitable rate. * Repeated simulation will generate the probability distribution of the PV of the cost of the option * Charge a premium having a PV which reflects the market cost of providing that guarantee (expected simulation cost plus a margin)

Question 30

What are typical mortality options that life insurers include in policies?

Answer 30

* The option to purchase additional benefits at normal premium rates without providing further evidence of health at the date the option is exercised. * The option to renew a life insurance policy at the end of its original term without providing additional evidence of health. * The option to change part of the SA from once contract to another.

Question 31

How can the LIC protect itself against mortality options?

Answer 31

* Ts & Cs under which the option can be exercised need to be clearly set out in the original policy - to reduce anti-selection (excess lives in poor health using the option to obtain large amounts of life assurance at premium rates that do not reflect their expected mortality) * Restricting times at which the option can be exercised: -- End of every 5 years of a 20-year TA -- At any time providing a qualifying event has occurred (birth, new job with higher salary) * Extent of the option will be specified - e.g. additional SA cannot be > original SA

Question 32

What is the cost of a mortality option?

Answer 32

* Excess of the premium that should have been charged for the additional assurance over the normal premium rate that is charged (in light of full underwriting information) -- For healthy lives – option will have little or no cost -- For unhealthy lives – option will generate considerable additional costs * Additional cost of an option depends on the health status of those who choose to exercise the option and the proportion of lives who choose not to exercise the option * The greater the proportion who exercise, the lighter the mortality experience. The smaller proportion who exercise, the worst the subsequent mortality experience.

Question 33

What are some factors that affect the cost of a mortality option?

Answer 33

SENATE * Selective withdrawals -- Healthy lives withdraw → same cost of option but loss of income * Extra costs to the PH who exercises the option -- Much higher premiums → healthy lives might shop around * Number of times the PH gets the chance to exercise the option -- Restrict → reduce anti-selection * Attaching conditions to exercising the option -- E.g. limit size of option; restrict % increase in sum assured * Term of policy with the option -- Longer term → greater chance of exercising option * Encouragement given to PHs to exercise the option -- We would want to encourage healthy lives

Question 34

How are mortality options normally valued?

Answer 34

Using CF projections. These CFs would include the additional: * Benefits expected to be payable under the option * Premiums expected to be received in relation to these benefits - based on the expected premium rates that would be charged to standard lives for the additional benefit, as at the option exercise date – PH that exercises option will pay exactly same premium as new PH * Expenses incurred in the administration of the option

Question 35

What are the extra assumptions required to value a mortality option?

Answer 35

* The probability that the option will be exercised, at each possible exercise date * The additional benefit level that will be chosen, if this is at the discretion of the policyholder * The expected mortality of the lives who choose to exercise the option * The expected mortality of the lives who choose not to exercise the option * The additional expenses relating to the option

Question 36

How would you determine the probability that the mortality option will be exercised?

Answer 36

* Conventional method → assume that all eligible PHs will take up the option, and that the maximum additional benefit will always be taken -- Advantage – Simplistic -- Disadvantage – Unlikely to be borne out in practise * North American method → uses more sophisticated take-up rate assumptions which vary by exercise date or by alternative option; these would ideally be based on past experience. -- Advantage – More realistic -- Disadvantage – Difficult to obtain data to make suitable assumptions

Question 37

How would you determine the expected mortality of those lives who will choose to exercise the mortality option?

Answer 37

* Typically, due to anti-selection, the expected mortality of lives who take up the option will be heavier than that of those who do not, example: -- Mortality of those who exercise the option may be assumed to be a higher percentage of the base mortality table, e.g. 150% of base mortality -- Alternatively, an age loading may be applied, e.g. age 𝑥 has 𝑥 + 5 mortality -- Or assume that mortality experience of those who will take up the option will be ultimate experience which corresponds to the select experience that would have been used as a basis if underwriting had been completed as normal when option was exercised - Approach for ‘conventional method’ above

Question 38

How would you determine the expected mortality of those lives who choose to not exercise the option?

Answer 38

* Could assume mortality experience will remain the same as without the existence of the option - However, this would mean average mortality for all lives has been assumed to be more than base mortality. * Find the mortality rates such that the average mortality for all lives remains at the base expected level