Chapter 27-Guarantees and 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

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

Answer 2

+Guaranteed minimum maturity value

(Can be used to back mortgage repayment)

+Guaranteed minimum surrender value

+Guaranteed annuity options

(Convert endowment proceeds to immediate annuity on guaranteed terms)

Question 3

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 3

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

+there’ll be a conflict between investing to meet guarantees, and investing for maximum performance

+Risk assumed by the life insurance company is that the backing assets will be insufficient to meet guarantees

+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

Question 4

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

Answer 4

generally, longer time-frame implies greater chance of 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 act on profit distribution levels if investment returns are disappointing

Question 5

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

Answer 5

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

Question 6

What kind of behaviour do we expect from PHs regarding exercising the guarantee? (2)

Answer 6

to only choose the option to take up the guarantee if it is ‘in the money’

alternatively meaning ‘if the guarantee bites’ ie is financially advantageous for them to do so

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 determine 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 swap floating rate returns at the option date for fixed returns sufficient to meet guaranteed annuity option (swaption)

Question 9

Describe the general principle behind stochastic simulation of investment performance to calculate the extra premium for an investment guarantee (2)

Answer 9

By projecting forward the value of the assets using a stochastic model and comparing this with the guaranteed sum payable, the insurance company can the measure the extent of additional cost incurred under a range of scenarios

Stochastic model of rates of investment returns can be used to simulate future asset prices.

Question 10

What 2 aspects are of crucial importance for stochastic simulations to be used to cost investment guarantees? (3)

Answer 10

key assumptions are evaluated carefully and should correspond with company’s planned investment strategy.

Key assumptions are the probability distribution of returns as well as the extent of option take up.

Large number of simulations are required to produce credible results.

Question 11

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

Answer 11

Determine the present value of the liability by discounting the simulated cost of exercising the option

Carry out multiple simulations to generate a distribution of the cost of providing the guarantee

Set the premium to the market cost of providing the guarantee i.e. the average simulated costs plus a margin

Question 12

Give common examples of mortality options offered by life insurers

Answer 12

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 date on which option exercise

Renew life insurance policy
eg term assurance, at end of original term
with no further evidence of health

Change benefit type
eg change part of a sum assured from one contract to another
eg from term assurance to endowment assurance

Question 13

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

Answer 13

The insurer can reduce anti-selection by

(1) ensuring that terms and conditions under which the option can be exercised are clearly set out in the original policy
(2) only allowing options to be exercised at specific points in time

every 5 years

anytime, provided a qualifying event has occurred eg childbirth, new job with higher salary

(3) specifying the extent of the option allowed’

eg additional sum assured cannot exceed original sum assured

Question 14

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

Answer 14

Cost of a 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

Cost roughly:
{proportion of lives exercising} * {ave health of lives exercising}

Question 15

What factors generally affect mortality options? (6)

Answer 15

(1) 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

(2) Number of times option available to exercise
eg every 5 years, every policy anniversary, any time whatsoever

(3) Conditions to exercise option
eg limiting size of option; restricting choice of contracts available for

(4) 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 business to good risks

care should be taken not to encourage poor risk lives

(5)Extra cost to PH exercising option

if option involves a steep increase in premiums, would cause healthier lives to shop around to get the same cover elsewhere

the company would lose out on potential profits from these healthy lives

(6) Selective withdrawals

healthy 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 a very long time but would still be left with remaining unhealthy lives who will exercise the option to cost of the company

Question 16

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

Answer 16

Cashflow projections would normally be used’

Cashflows include addtional benefits and premiums expected to be paid in relation to the option

Cashflows allow for 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 option exercise date

Allow for additional expenses relating to option eg writing to PH to remind of option

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

Question 17

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

Answer 17

probability that option will be exercised, at each possible exercise date i.e. take-up rate

additional benefit that will be chosen, if at discretion of PH

expected mortality of lives who choose to exercise option

expected mortality of lives who choose not to exercise option

additional expenses relating to option

Question 18

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

Answer 18

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 maximum 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 19

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 19

For mortality of lives who do not take up the option

(1) 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 to experience higher than base mortality)

(2) 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