Chapter 28: Pricing

Question 1

Critical illness incidence rate

Answer 1

P(contracting one of the specified critical illnesses)

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

Question 2

Critical illness claim incidence rate (risk premium for a stand alone CI)

Answer 2

P(claiming on your CI contract as a result of contracting one of the specified critical 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 and disadvantages of multi-state modelling

Answer 6

ADV:
1) Tracks policyholders separately
2) Allows for sensitivity testing

DISADV:
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 7

Transition rates may be a function of…

Answer 7

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

Question 8

Total estimated claims outgo per month

Answer 8

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

Question 9

Sickness inception rate

Answer 9

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

Question 10

Claims inception rate (three variations)

Answer 10

It is the probability that a claim will become payable to an individual in the year of age x to x+1. This corresponds to the end of the deferred period.

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

1) initial claim inception rate
probability of claim inceptions (following a deferred period d) occurring during the year of age [x, x+1]

2) central claim inception rate (a)
expected number of claim inceptions occurring over the year of age [x, x+1] (following deferred period d)

3) Central claim inception rate (b)
expected number of sickness inceptions occurring over the year of age [x, x+1], which subsequently become claim inceptions d years later

Question 11

When would sickness and claim inception rates be equal

Answer 11

When there is no deferred period, so that the benefit payments commence immediately as the policyholder falls sick

Question 12

What is the difference between sickness inception rates compared to claim inception rates, and how is it viewed in an income protection world

Answer 12

Sickness inception rates relate to when individuals fall sick. In an income protection insurance context, this corresponds to the point in time when the individual is first deemed unable to work

Claim inception rates relate to the point in time at which benefits payments commence. In an income protection context, this corresponds to the end of the deferred period

Question 13

What is the Inception/disability life annuity approach

Answer 13

Simplified multi-state model approach - where multi-state model is converted into multiple decrement table format

It considers two functions:
1) the claim inception rate
- It is the probability that a claim will become payable to an individual in the year of age x to x+1
- = sick inception rate x P(remain sick past the deferred period)

It is derived from sickness inception rates by multiplying the probability of sickness inception by the probability of remaining sick throughout the deferred period

2) The disabled life annuity
- It is the present value at the date of claim inception of expected claim payments to individuals disabled after the deferred period until policy expiry, recovery or death
- it is based on a double decrement table (death and recovery)

3) Survival probability
probability the policyholder will be eligible to claim in a certain year

Question 14

Expected claim cost formula for income protection

Answer 14

EPV = EligibilityProbability×ClaimInceptionRate×DisabilityAnnuity×DiscountFactor×Benefit

Question 15

When estimating CI incidence rates from population medical records, what is a potential problem that must be addressed?

Answer 15

Double counting, where an individual with multiple diseases is counted under each cause, leading to an overestimation of the total incidence rate.