27. Cost of guarantees and options

Question 1

Name examples of investment guarantees

Answer 1

1. Guaranteed minimum maturity values
2. Guaranteed minimum surrender value
3. Ability to convert lump sum into annuity or vice versa on guaranteed terms

Question 2

What is the risk introduced by issuing guarantees?

Answer 2

• At specified future times, assets backing liabilities won’t be enough to meet guarantees.

Question 3

What is the liability created by an investment guarantee?

Answer 3

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

Question 4

How can guarantees be valued?

Answer 4

o Option-pricing techniques aka market valuation
o Stochastic simulation of investment performance

Question 5

Explain how a guarantee can be valued using option-pricing techniques:

Answer 5

o Options in a life company are analogous to options traded in market
o Analogies:
o Guaranteed minimum maturity value: European put with strike price being min MV
o Guaranteed minimum surrender value: American put with strike price being min MV
o Guaranteed annuity rate: call option on bonds that would be necessary to ensure guarantee is met or …
o … option to swap floating rate returns at option date with fixed rate returns sufficient to meet guaranteed annuity optio
o May be difficult to value whole investment fund with one traded option, can use options written on market indices for bonds and equities as approx.
o On policy issue date, all guarantees out of the money as current market rates are sufficient to meet guarantees
o Will have time value based on market view of the present value of likely future costs of option
o So suitable option’s market price can be used to value option/guarantee

Question 6

Explain how a guarantee can be valued using stochastic simulation

Answer 6

o Use stochastic model of rates of return to simulate future asset prices.
o Assumptions in model must correspond with company’s planned investment strategy
o Must perform large number of simulations for reliable estimates
o Liability may be fixed if guarantee is taken (e.g. maturity guarantee)
o Liability may depend on future market conditions (e.g. guaranteed annuity rates)&raquo_space;
o … factors influencing A and L will be simulated
o If w/profits, must also make assumptions about future bonus declarations and must be consistent with simulated asset performance
o Need assumptions about future rates of taking up options taking into account expected ph behaviours and size of guarantee relative to benefit
o PV of L is discounted simulate cost of exercising option at suitable rate.
o Repeat simulations&raquo_space; probability distribution of present value of cost of option.
o Premium = present value reflecting “market cost” of providing guarantee, could be expected simulated cost plus margin

Question 7

Give examples of mortality options

Answer 7

o Buy additional benefits without proof of further underwriting and normal premium rates at date when option is exercised
o Renew life policy, e.g. term assurance at end of original term without further underwriting
o Change part of sum assured from one contract to other e.g. term assurance to endowment

Question 8

What are the implications of including options for insurer?

Answer 8

o Terms under which option can be exercised must be clearly set out in original policy
o Extent of option must also be specified e.g. additional sum assured can’t exceed original sum assured
o T&Cs are designed to reduce selection against office

Question 9

What is the cost of an option?

Answer 9

o Value of excess of premium that should in light of full uw info have been changed for additional assurance, over normal premium rate that’s charged
o If life exercising is in good health and satisfies normal uw, option generates little/no additional costs.
o If life exercising is in poor health, option generates additional costs.
o Total expected additional costs depend on:
o Health status of those exercising
o Proportion exercising (more people exercising = subsequent mortality will on
average be less extreme)
o Roughly:
o [prop exercising option] x [ave health of people exercising]

Question 10

What are the factors affecting mortality options?

Answer 10

o Term of policy. Longer term = more likely will exercise at some time
o Number of times can exercise option
o Conditions attaching to exercise (e.g. limit size of option)
o Encouragement of ph to take up option
o Extra cost to ph exercising option
o Selective withdrawals. Withdrawal by healthy lives before option date reduces income expected to be received from risk pool

Question 11

Explain how you’d value a mortality option

Answer 11

o Usually use cashflow projections
o Cashflows include additional benefits expected to be payable and expected premiums expected to be received under option to extent to which we assume option is taken up
o Additional premiums based on expected premium rates charged to standard lives for additional benefit at exercise date
o If used for pricing, must make allowance for extra reserves held before and after exercise date
o Extra assumptions:
o Probability of option being exercised at each exercise date
o Additional benefit level chosen (if chosen by ph)
o Expected mortality of those exercising
o Expected mortality of those not exercising
o Expenses relating to option

Question 12

How can option take up rates be determined?

Answer 12

1. Assume all eligible ph will take up option and that max additional benefit is always chosen
2. If multiple possible exercise dates, may assume worst option from company’s financial p.o.v is always chosen
3. Use sophisticated take up rate assumptions varying bu exercise date or alternative option, ideally based on past experience.

Question 13

How can mortality rates be estimated when costing an option?

Answer 13

• Expected mortality of lives taking up option is heavier than that of those who aren’t because of anti-selection.
• Can assume mortality of those exercising is a higher % than base mortality table
• Age loading may be applied e.g. age x&raquo_space; age x + 5
• May assume mortality of those taking up option will be ultimate experience corr to select experience that would have been used if uw was done as normal when option was exercised. (Consistent with all eligible ph taking up option)
• May assume mortality of lives not taking up option is same level as would have been without option. However, implies average mortality of all lives is in excess of base mortality
• May assume mortality of those not taking up option is s.t average mortality is the same as the base table, i.e. not taking up option = lower than base mortality

Question 14

Describe how you’d stochastically simulate an investment guarantee

Answer 14

• Mostly model future returns stochastically
• Select appropriate distribution functions and parameters that represent likely future experience
  
  • e.g. lognormal can be used and back tested to find suitable approaches
  • or buy simulated returns that have been modelled appropriately
• Project unit fund to maturity for each simulation on the minimum guaranteed return and projected investment returns
• Cost of guarantee is the difference of two fund values at maturities if projection > minimum maturity value
• If projected investment returns MV > min investment return MV&raquo_space; cost is zeo
• Average across all simulations is expected cost of guarantee
• Must run sufficient number of simulations to give credible results.