27 Cost of Guarantees and Options Flashcards
How is investment return guaranteed in without-profits and non-linked business.
Guaranteeing a sum assured or annuity benefit derived from a premium formula based on a yield of x% pa means that a guaranteed return of x% pa is guaranteed.
Investment guarantees
Examples
The blow examples hold for with-profit, linked and non-linked contracts
- a guaranteed minimum maturity value
- a guaranteed minimum surrender value (again, in money terms)
- a guaranteed annuity option
Investment guarantees
Implications for the insurance company
- Risk: at specified times in the future the “backing” assets will be insufficient to meet the guarantees.
- Risk is increased where policyholders has a choice whether and when to exercise the option
- conflict between investing to meet the guarantees and investing for maximum performance. (If the company has control over the investment policy)
- Unit-linked: Company has no control over the investment policy, must include the cost of the guarantee in the original charges to the extent that the guarantee will not be matched
- The risk to the company will depend on the outstanding term of the policy
Valuing an investment guarantee
Guarantee liability = guaranteed amount - the cost that would have been incurred in the absence of the guarantee
P/h should only exercise in-the-money options
Methods:
- option-pricing techniques
- stochastic simulation of investment performance
Valuing an investment guarantee
Use of option-prices/market valuation techniques
options incorporated into life insurance contracts are analogous to options traded in the market place.
* guaranteed minimum maturity value = (European style) put option on the investment funds at an exercise price corresponding to the maturity guarantee
* guaranteed minimum surrender value = American style option or a series of options with different exercise prices which match the guaranteed surrender values.
* guaranteed annuity rate = a call option on the bonds that would be necessary to ensure the guarantee was met, ie at an exercise price which generates the required fixed rate of return. Alternatively, an option to swap floating rate returns at the option date for fixed rate returns sufficient to meet the guaranteed annuity option (a “swaption”)
If invested in bonds to match future annuity option: purchase a bond put option. If interest rates rise, market values will fall. At risk of being unable to meet maturity benefit if option is not taken up. Put option allows LI to sell bonds at exercise price (maturity value).
how can insurance company protect itself from the annuity rate guarantee
purchasing call options on bonds
- maturity the insurance company will have cash available equal to the open market cash option
- If interest rates are lower than those used in guaranteed annuity rates, then bonds needed to match annuity payments will cost more than the amount available
- call option fixes a maximum purchase price for the bonds at the exercise date
- the current market price of the call option represents the expected cost of the annuity rate guarantee
how can insurance company protect itself from the annuity rate guarantee
purchasing interest rate swap options
- buy options “receive fixed/pay floating” swaps as from the retirement date
- the fixed rate equal to the interest rate in the guaranteed annuity basis
- swap being undertaken if bond yields had fallen below the guaranteed rate at the retirement date
- swap agreement will pay the insurer the income shortfall on its (cash) returns
- up to the level of income required to cover the guaranteed annuity payments
- current market price of the necessary swap options that represent the market valuation of the annuity rate guarantee
Valuing an investment guarantee
Stochastic simulation
- stochastic model of rates of return on investments is used to simulate the future price of assets
- assumptions (prob distribution for investment returns) must correspond to the company’s planned investment strategy
- assumptions needed about future rates of exercising options, taking account expected policyholder behaviour and the size of the guaranteed amount relative to the alternative benefit
- large number of simulations is needed in order to obtain reliable estimates.
- For each run, we can calculate the projected unit fund (WOP: asset share for a given level of premium)
- then compare the unit fund against the guaranteed minimum maturity value (sum assured)
- if guarantee bites, cost = guarantee amount - fund
- if it doesn’t bite. cost = 0
- average cost over all runs, discount if needed to get expected cost of guarantee
- plus a margin
- WOP: premium should then be varied until the probability and amount of loss are acceptable
- for some guarantees, the liability will dpend on future market conditions, that will also have to be simulated
- e.g. guaranteed annuity options: need to project market bond yields at maturity date
- WP business - model needs to include assumptions about the level of future profit declarations (consistent with asset performance)
Mortality options
Examples
- purchase additional benefits without providing further evidence of health at the normal premium rates at the date on which the option is exercised
- renew a life insurance policy, eg a term assurance at the end of its original term without providing additional evidence of health
- change part of the sum assured from one contract to another, eg from term assurance to endowment assurance
Mortality options
Implications for the insurance company
- terms and conditions under which the option can be exercised need to be clearly set out in the original policy
- Sometimes: can only be exercised at fixed points of time
- The extent of the option will also be specified, eg the additional sum assured cannot exceed the original sum assured.
- terms and conditions designed to reduce “selection against the office”
- total expected additional costs of an option depend on the health status, and the proportion of lives who choose to exercise the option
Mortality options
Valuing a mortality option
cost of an option = premium that should, in the light of full underwriting information, have been charged for the additional assurance - the normal premium rate that is charged
* normally valued using cashflow projections
* cashflows would include the additional benefits expected to be payable under the option and the additional premiums expected to be received in relation to these benefits
* additional premiums would be based on the expected premium rates charged to standard lives at excercise date
* allow for any additional expenses incurred in the administration of the option
* Pricing: allowance should also be made for the additional reserves that should be held
* Assumptions:
* - option take-up probabilties
* - additional level of benefit to be chosen
* - expected mortality of those who do and do not take up the option
* - additional expenses relating to the option
factors affecting mortality options
- The term of the policy with the option (longer term = higher cost)
- The number of times the policyholder gets the chance to exercise the option
- Conditions attaching to exercising the option
- encouragement given to policyholders to exercise the option
- The extra cost to the policyholder who exercises the option (large increases in premium will discourage healthy lives)
- Selective withdrawals. Withdrawal by healthy lives before the option date reduces the income (extra premiums) that we would have expected to receive from the whole risk pool
Valuing a mortality option
Assumptions: Option take-up rates
- may assume that all eligible policyholders will take up the option
- the maximum additional benefit will always be taken
- assume that the worst option from the financial point of view of the company is chosen with probability one
- Alternatively, more sophisticated take-up rate assumptions which vary by exercise date or by alternative option. based on past experience.
Valuing a mortality option
Assumptions: Mortality rates
due to anti-selection, the expected mortality of lives who take up the option will be heavier than that of those who do not
there should be a link between the assumed option take-up rates and the assumed mortality rates
Three possible approaches:
1. Take up mort: higher percentage of the base mortality table, OR age loading
2. Ultimate experience which corresponds to the Select experience that would have been used as a basis if underwriting had been completed. (consistent with an assumption that all eligible policyholders take up the option)
3. Alternative: mortality of those who do not take up the option is such that average mortality for all lives remains at the base expected level.
