22. Pricing (4) - Options and Guarantees

Question 1

Mortality and morbidity (health) options

Answer 1

to the extent the option might be exercised by someone in poor health, the insurer will bear a cost
- the difference between the ordinary premium rate granted and that which would have been granted had the life been underwritten
- investment guarantees not the norm in health and care policies

Question 2

Cost of option

Answer 2

value of excess premium that should, in light of full underwriting, have been charged for the additional insurance over the normal premium rate charged
- cost of a health option ~ (proportion of lives exercising option) x (average extent that health of lives exercising the option is worse than normal)

Question 3

Factors affecting health options

Answer 3

• term of the policy (longer –> p/h longer to exercise)
• number of times policyholder has to exercise option
• conditions attaching to exercise of the option
• encouragement given to p/h to exercise - if take-up low, tends to be only those who have most to gain from exercise
• extra cost to policyholder who exercises options (e.g. increase in premiums steep, healthier policyholders may opt to take out cover elsewhere for cheaper)
• selective withdrawals (withdrawal by healthy lives before option data reduces the income would have been expected to receive from the whole risk pool)

Question 4

Courses of action company might follow for onerous option

Answer 4

• reduce encouragement given to policyholders to exercise the option
• reinsure some of the increased risk
• remove option for new business
• increase standard premium rates
• make option less attractive to reduce take-up rate
• limit number of times the option can be exercised

Question 5

Valuing a mortality/ morbidity option

Answer 5

Requires extra assumptions as part of the pricing basis
- probability the option will be exercised
- expected mortality/ morbidity of the lives who choose to exercise the option

Two methods
- North American method
- conventional method

(stochastic modelling - third method establish core cost of option)

Question 6

North American method

Answer 6

requires extra data on likelihood of option being exercised and morbidity of those doing so
- double or triple decrement table for lives who have not yet exercised the option
- mortality/ morbidity table for lives who have exercised the option

• often difficult to obtain sufficient data to estimate all decrement rates required
• for new LoBs, there will be no direct experience

Question 7

Conventional method

Answer 7

• assumes all lives eligible to take up the option will do so
• mortality of those who take up the option will be the Ultimate experience, corresponding to the Select experience that would have been used as a basis if underwriting had been completed as normal when the option was exercised
• ## copes less easily with multiple options

Question 8

Stochastic modelling

Answer 8

• future experience projected and numbers taking up various options and subsequent claim propensities are investigated
• subdivide population of policyholders into different risk categories
• proportions ending up in each risk group, average claim experience of each risk group at option date could be modelled as stochastic variables
• require probability distributions for these