Pricing Health And Care Contracts

Question 1

Critical illness incidence rate

Answer 1

P(contracting one of the specified critial illnesses)

For example….
i_x
= i_x^heart attack
+ i_x^stroke
+ i_x^cancer

Question 2

Critical illness claim incidence rate

Answer 2

P(claiming on your CI contract as a result of contracting one of the specified critial illnesses)

P(contracting illness) x P(surviving survival period)

Question 3

Accelerated critical illness claim incidence rate

Answer 3

P(pay-out due to the earliest of CI or death)

= (i_x) + (1 - k_x) q_x

Where k_x is the proportion of total deaths in age [x - x+1] that are due to critical illnesses specified in the policy

Question 4

List the two methods of pricing LTCI and IP policies

Answer 4

1) Multi-state modelling
2) Claim inception and disability annuity approach

Question 5

Multi-state modelling

Answer 5

Policyholders are separately tracked through the different states of healthy, sick, sick within the deferred period, sick and claiming, lapsed and dead.

Assumed forces of transition between states are derived from data and used to project the probabilities of being in particular states at particular future times.

These probabilities are then used in conjunction with an interest rate assumptions in a discounted cashflow model to value benefits and obtain a price.

Question 6

Advantages of multi-state modelling

Answer 6

1) Tracks policyholders separately
2) Superior tool for sensitivity testing

Question 7

Disadvantages of multi-state modelling

Answer 7

1) Many sub-cohorts can be identified, necessitating many transition probabilities
2) This leads to high data requirements
3) It also means calculation is time-consuming
3) It may lead to spurious accuracy

Question 8

Transition rates may be a function of…

Answer 8

1) Previous illnesses
2) Age - x
3) Duration in stage

Question 9

Total estimated claims outgo per month

Answer 9

Sum across all groups of
(average sum assured of group) x (number of lives in group)

Question 10

Sickness inception rate

Answer 10

The probability of falling sick. This corresponds to the point in time when the individual is first deemed unable to work

Question 11

Claims inception rate

Answer 11

The probability of making a claim. This corresponds to the end of the deferred period.

Claims inception rate =
(sickness inception rate) x (probability of remaining sick throughout the deferred period)