Ch 27: Cost of investment guarantees and mortality options

Question 1

Why are investment guarantees useful? (3)

Answer 1

• Traditional life insurance contracts transfer mortality, expense and investment risk from the policyholder to the life insurance company.
• Unit linked and index linked contracts leave the investment risk with the policyholder
  
  • but these contracts’ attraction can be enhanced if part of the investment risk is transferred to the company by the company offering guarantees to protect the policyholder from the downside risk.

Question 2

Give examples of investment guarantees, as well as brief descriptions (3)

Answer 2

Guaranteed min maturity value

• guaranteed amount in monetary terms (for investment linked contracts)
• guaranteed amount in monetary terms for non-linked contracts
  
  • eg non linked with profit endow assurance used to back mortgage
  • very attractive, where eventual maturity unknown; could guarantee basic sum assured + bonuses >= certain value (set to size of mortage )

Guaranteed min surrender value

• give a guaranteed amount in monetary terms

Guaranteed annuity options

• convert endowment proceeds to annuity on guaranteed terms
• PH takes cash maturity value, can choose to buy immediate annuity from insurer at rate guaranteed at policy inception
• attractive if PH worried annuity may become more expensive at retirement

Question 3

What is the key risk/implication for an insurer that offers contracts with investment guarantees? (1)

What makes the above key risk even more difficult to control? (2)

Answer 3

The key risk/implication for insurers offering investment guarantees is that at specific times in future, assets backing the guarantees are insufficient to meet the guarantees. Guarantee Bites

This key risk becomes particularly diffcult to control of PH has choice over whether to exercise option

• annuity guarantee: gives PH choice btwn cash or income at maturity.
• surrender value guarantee: insurer won’t know when surrender might happen

Question 4

For insurers who have control over investment policy, what conflicts arise by providing investment guarantees ? (2)

What steps must insurer take to meet guarantees if it chooses not to invest to match the guarantees? (2)

Answer 4

Where insurer has control over investment policy (eg conventional, non linked contracts) conflicts due to investment guarantees arise in terms of

• conflict between investing to match guarantees, and investing for maximum returns
• eg if insurer providing with profits contracts, invests in backing assets to meet minimum guarantee, then all PH will recieve is this minimum return. may as well have just bought a without-profits contract

If company chooses to invest such that it doesn’t match guarantees,
* it must include cost of guarantee in original pricing basis
* if company has no control over investment policy (eg unit linked) , then to extent that guarantee will not be matched it must include cost of guarantee in original charges
* + prem/charges to offset risk

Question 5

What impact does time/outstanding term play on risks faced by insurer due to offering investment guarantees (2)

Answer 5

Risk from investment guarantees depends on timeframe/outstanding term

• generally, longer timeframe=> greater chance things go wrong vs current forecasts eg offering guarantee annuity rate for 5 years, vs 20 years
• for with profits business, actually tricky to say: longer term may give insurer time to take corrective action with management actions

Question 6

When valuing an investment guarantee, we need to consider the “liability created by that investment guarantee”; what does this mean? (2)

Answer 6

The liability created by the investment guarantee is

• the excess of the guaranteed amount (guaranteed maturity value/guaranteed surrender value/fund needed to purchase ‘guaranteed annuity’ at current market rates) over
• the cost that would’ve been incurred at the time in the absence of the guarantee
• Assume PH take option if it is in the money (bites for insurer)

Question 7

How do insurer’s meet the cost of the liability created by the investment guarantee? (1)

What methods are available to price the costs of the guarantee? (2)

Answer 7

Insurer’s meet the cost of the additional liability created by the guaranteed by

• charging an extra premium to reflect the extra sums it may need to pay due to the guarantee biting

To determing the extra premium to charge, the insurer can use

• option pricing techniques
• stochastic simulation

Question 8

Describe the general principle behind option pricing techniques to calc the extra premium for an investment guarantee (1)

Give examples of options which can be used to meet the different investment guarantees insurers may offer (6)

Answer 8

Option pricing/market valuation techniques assess the extra premium by

• looking at market price of derivative/option insurer could use to mitigate risk

Options which can be used to mitigate the following investment guarantees

• guaranteed maturity value
  
  • European style put option on investment funds at an exercise price = maturity guarantee
• guaranteed surrender value
  
  • similar American style put option/series of puts with different exercise prices which match guaranteed surrender values
• guaranteed annuity rate
  
  • call option on bonds that are needed to ensure guarantee is met
  • ie at exercise price which generated the required fixed rate of return
  • can also be mirrored by option to swop floating rate returns at the option date for fixed returns sufficient to meet guaranteed annuity option

Question 9

Once we’ve obtained a suitable option/derivative to hedge the risk of the investment guarantee, what does this provide? (2)

What difficulty may arise with the insurer’s investment fund compared to the market used to determine the premium for the investment guarantee? (2)

Answer 9

The market price of a suitable option produces a way of costing a financial guarantee or guarantee incorporated in a life insurance policy

• the insurer doesn’t actually necessarily purchase said option (that is a seperate matter, depending on the investment strategy)
• however, we now have a suitable price to charge for the investment guarantee

In practice, it is quite difficult to

• ensure that the insurer’s whole investment fund corresponds to a single option traded in the market
• to overcome this, an approximation is possible by using options written on market indices for equities and bonds

Question 10

What are our expectations regarding whether the investment guarantee provided will be in the money or out of the money at policy issue? (4)

Answer 10

At policy issue, the investment guarantee will normally be

• out of the money
  
  • Current market rates are more than sufficient to meet the guarantees, but will have a time value which is the result of views of the market of the present value of the likely future costs of the option.
• however, the guarantee may very well be in the money
  
  • e.g. current yields may be historically so low that a life insurance company would be happy to provide a guarantee at a future date based on a higher yield (with the expectation that it may be out of the money at the future date).

Question 11

Describe the general principle behind stochastic simulation of investment performance to calc the extra premium for an investment guarantee (3)

Answer 11

Stochastic simulations of investment returns to price extra premium

• Proj assets and comp with guar benefit=>
• the extra sums likely to be needed under the guarantee by simulating a range of investment scenarios
• a model of rates of return on investments is used to simulate the future price of assets, and we can compare this to the guaranteed sum payable

Question 12

What 2 aspects are of crucial importance for stochastic simulations to be used to cost investment guarantees? (6)
Basis
Simulations

Answer 12

When stochastically simulating cost of investment guarantees, it is important that

• key assumptions are evaluated carefull and should correspond with company’s planned investment strategy.
  
  • key assumptions are
    
    • probability distribution used to model investment return
    • mean
    • variance
    • option take up, that needs to take account of PH behaviour and size of guaranteed amount relative to asset share
• we run a large number of scenarios/simulations to obtain reliable estimates

Question 13

Describe the output from stochastic modelling? (3)

Answer 13

The key principle from stochastic modelling is as follows

• stochastic modelling will produce a distribution of results for the cost of the guarantee
• hence, the simulated average cost is an estimate of the expected value (for the cost) of the guarantee
• is is only an estimate, because there may still be random error, error in the structure of the model, or errors in the value of the parameters used

Question 14

When using stochastic modelling to calculate the cost of the guarantee, how do we deal with issues surrounding guarantees which are ‘fixed’ vs guarantees which ‘vary’? (5)

Answer 14

For some guarantees, the liability generated if the guarantee is taken (or of the guarantee bites) may be

• fixed: eg maturity guarantee
• dependant on future market conditions: eg guaranteed annuity rates
  
  • for these, factors influencing the value of the liabilities as well as assets will need to be simulated
  • for guaranteed annuity rates, project market bond yields
  • for with profit contracts, assumptions about future profit declarations

Question 15

Once we’ve run our stochastic simulations, what would be the final step to calculate the amount to charge for providing the investment guarantee? (3)

Answer 15

For the final step, we

• discount the simulated cost of exercising the ‘option’
• repeated simulation will generate the probability distribution of the present value of cost of the option.
• then charge premium having a present value which reflects the market cost of providing guarantee (expected simulated cost plus margin).

Question 16

Give common examples of mortality options offered by life insurers

Answer 16

Common examples of mortality options include

• Purchase additional benefits
  
  • with no further evidence of health at normal premium rates
  • for a life of that particular age at the option date
• Renew life insurance policy
  
  • eg term assurance, at end of original term
  • with no further evidence of health
• Convert policy
  
  • eg change part of a sum assured from one contract to another
  • eg from term assurance to endowment assurance

Question 17

Mortality options give great scope for anti-selection against the insurer; how might the insurer reduce this with policy wording/conditions? (5)

Answer 17

The insurer can reduce anti-selection by

• ensuring that terms and conditions under which the option can be exercised are clearly set out in the original policy
• only allowing options to be exercised at specific points in time
  
  • every 5 years
  • anytime, provided a qualifying event has occured eg childbirth, new job with higher salary
• specifying the extent of the option allowed
  
  • eg additional sum assured cannot exceed original sum assured

Question 18

The presence of mortalty options comes with a cost. Describe the cost to the company of a lfe insurance policy mortality option (6)

Answer 18

Cost of a life insurance policy mortality option

• Cost = Prem w/ u/w - Prem 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
• Cost roughly:
  
  • {proportion of lives exercising} * {avg health of lives exercising}

Question 19

What factors generally affect the cost mortality options? (6)

Answer 19

• Term of policy with option
  
  • longer term, longer PH will have option, and more likely that at some time their health will make option appear worthwhile
• Number of times option available to exercise
  
  • eg every 5 years, every policy anniversary, any time whatsoever
• Conditions to exercise option
  
  • eg limiting size of option; restricting choice of contracts available for
• Encouragement given to exercise option
  
  • low take up=> only those with most to gain will exercise
  • encouraging healthy lives to exercise will not cause any additional expected loss + should contribute to insurer’s total profit as it issues busines to good risks
  • care should be taken not to encourage poor risk lives
• Extra cost to PH exercising option
  
  • if option involves steep increase in premiums, would cause healthier lives to shop around to get same cover elsewhere
  • company would lose out on potential profits from these healthy lives
• Selective withdrawals
  
  • healthly life may cancel 10 year renewable term assurance after 2 years if cover without option is much cheaper
  • option loading has not been collected for very long time but would still be leff with remaining unhealthy lives who will exercise option to cost of the company

Question 20

Describe how a mortality option would be valued? (6)

Answer 20

1. Cashflow projections would normally be used
2. Cashflows include addtional benefits and premiums expected to be paid in relation to the option
3. Cashflows allow for extent to which the option is assumed to be taken up
4. Additional premiums based on the expected premiums to be charged at option exercise date to normal lives
5. Allow for additional expenses relating to option eg writing to PH to remind of option
6. If purpose of valuation is to price option (rather than setting liability), then need to allow for additional reserves that should be held, both before and after exercise

Question 21

List 5 additional assumptions required to price a contract if a mortality option is added (5)

Answer 21

1. probability that option will be exercised, at each possible exercise date
2. additional benefit that will be chosen, if at discretion of PH
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 22

Describe two methods that can be used to value mortality options, in regards to option take-up rates and mortality (6)

Answer 22

North american method

• assume more sophisticated take-up rates which vary by exercise date or by alternative option
• would ideally be based on past experience

Conventional method

• assumes all eligible PHs will take up option (unlikely to be born in practice), and that maximium additional benefit will always be taken
• if there are several alternative options or exercise dates, model may assume worst option from company’s financial POV is chosen with probability one
• assume the mortality experience for the take up lives is ultimate
• this method is possible when there’s a single option date

Question 23

What may we assume for mortality regarding those who do take up the option? (5)

Answer 23

For mortality of lives who do take up option

• typically, due to anti-selection, expected mortality of lives who take up the option will be heavier than that of those who do not eg
  
  • a higher percentage of the base mortality table eg 150%
  • age loading eg for PH aged x, use x+5 mortality
  • assume ultimate mortality
    
    • this would be consistent with assumption that all eligible PHs exercise option (i.e. conventional method described earlier, not North American)

Question 24

What are 2 alternative assumptions that are typically made regarding the mortality of those lives that don’t take up a mortality option? (4)

Answer 24

For mortality of lives who do not take up the option

• Assume lives that don’t 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 ro experience higher than base mortality)
• Assume that mortality of those who don’t take up option us such that average mortality for all lives remains at the expected base level.
  
  • here, the assumed mortality of those who do not take up the option would be less than (1), ie less than base mortality