Chapter 21-Setting Assumptions (1)

Question 1

Background on assumptions

What is the key reason assumptions are used for? (1)

What key risk does setting assumptions introduce? (1)

What kind of risks can be somewhat mitigated by appropriate matching of assets? (3)

Answer 1

Assumptions used by insurers for variety of reasons, mostly assessing eventual cost of liabilities

Setting assumptions may => parameter risk: want to reduce this

Not easy finding matched assets protecting from actual experience different to expected, can sometimes reduce following risks from investment matching:

(1) Investment risk: relates return required meet current liabs for future payouts
(2) Inflation risk: relates increase in inflation-linked liabs + liabs behaving approximately in line with inflation (eg expenses)
(3) Marketing risk: ability to satisfy PHs in relation to any investment-linked/discretionary benefits.

Question 2

Best estimate mortality:

List 2 separate parts of mortality to be considered when setting best estimate mortality assumptions (2)

Answer 2

Base mortality: initial rate of mortality, the main demographic assumption for pricing/evaluating life insurance contracts

Mortality trend: how mortality rate changes over time

Question 3

Best estimate mortality:

Outline a general process for setting assumptions (5)

Answer 3

(1) Investigate past experience; make past best estimate parameters; appropriate in context of historical conditions/then-circumstances
(2) Consider future conditions (including commercial and economic environment ) during period for which assumptions will be used
(3) Determine future best estimates assumptions, given expected future conditions
(4) Extent of (a) relying past data vs (b) allowing for other factors, depends on data credibility/relevance + parameter’s predictability
(5) Adjust best estimates with margin. Size of margin depends on:

+purpose for which model is required

+degree of risk associated with parameter

Question 4

Two factors that a company needs to balance in deciding on the appropriate number of years of past experience to include in a mortality investigation.

Answer 4

Need to balance the following:

+Adequate volume of data to ensure credibility

+The heterogeneity of the data due to trends over time which may not be relevant

Question 5

Best estimate mortality: base mortality derivation

Describe how to derive best estimate base mortality rates, in terms of What factors will influence future mortality experience (3)

Answer 5

Rates should reflect expected future experience of lives to be insured by contract being priced, in terms of

(1) target market: affected by distribution channel
(2) underwriting controls:
(3) change: since last historical investigation, to point assumptions will apply on average (usually 10 - 15 yrs)

Question 6

Best estimate mortality: base mortality derivation

Describe how mortality rates are set including adjustments (7)

Answer 6

Base rates usually uses adjusted rates from standard table

(1) saves resources
(2) protects against errors eg inappropriate graduation
(3) sufficient data: analysis own experience=> derive adjustments
(4) data must be over enough years (adequate volume), but also few enough years (prevent excessive heterogeneity from trends over time)
(5) analysis divide data into relevant homogenous groups
(6) further adjustments if different experience expected from that which analysed data relate (targ market, underwrit, distr)

Question 7

Best estimate mortality: base mortality derivation

What data sources can be used to adjust base mortality rates (6)

Answer 7

own past experience with that product,

own past experience with similar product(s),

reinsurance data

industry data i.e. standard tables

international data

national statistics

Question 8

Best estimate mortality: base mortality derivation data sources

In using data for adjustments when deriving best estimate base mortality rates, list some pros/cons related to the following data sources which may be used:

Industry wide investigations (3)

Population mortality statistics (2)

Reinsurer data (5)

Answer 8

(1) Industry wide investigations
useful for contracts where

+insufficent volumes of own experience exist

+good for showing trends, since trends in own data might be due to statistical variation

+not 100% suitable since not based on insurer’s particular PHs

(2) Population mortality statistics

+useful for showing trends if re-examined at regular intervals in past

+not 100% suitable since not based on insurer’s particular PHs

(3) Reinsurer data
Ads
+access to mortality experience of many direct writers

+may be most relevant data available
Disads

+relates to large number of different companies

+may have little/no suitable data

+comes with a cost: cost of reinsurance

Question 9

Best estimate mortality: mortality trends

What do we mean by ‘mortality trend’? (1)

State 2 circumstances where the estimation of future mortality improvements is particularly important (2)

Answer 9

The mortality trend relates to how the rate of mortality changes over time.

Estimating future mortality improvements is particular important:

(1) for policies with longevity risk e.g. annuities
(2) when rates are guaranteed rather than review-able

Question 10

Describe how we might consider expected changes in mortality over time

Different approaches used to project mortality trends (3)

Considerations to the product (2)

Answer 10

(1) expectations: uses expert opinion + subjective judgement to specify range of future scenarios

+can implicitly include all relevant knowledge, including quantitative factors

+subjective and subject to bias

(2) extrapolation of historical trends
+project historical mortality trends into the future

+some subjectvity: choice of period to determine trends

(3) explanatory projection techniques,

+modelling bio-medical processes that cause death

+only effective to extent process understood and mathematically model-able

Considerations should also be given to the product e.g.
important for contracts +paying significant death benefit
+important for annuities where increased longevity is a risk
+not important for single premium savings contracts

Question 11

Best estimate mortality: mortality trends

State how each of the following might be taken into account when making projections of future mortality:

(1) cohort effect
(2) the combined effects of multiple factors
(3) random effects

Answer 11

(1) Cohort effect
each year of birth cohort is modelled separately, allowing for specific mortality improvement rates by cohort (as well as by age and sex)

(2)Multi-factor effects
Use multi-factor predictive modelling techniques (eg. generalised linear models), accounting for personal attributes along with external factors affecting mortality, allowing for any correlations and interactions between them.

(3) Random effects
Use stochastic modelling (e.g. Lee-Carter or P-spline method)

Question 12

Morbidity assumptions

What factors/kind of rates should we consider when setting morbidity assumptions (4)

Answer 12

Key factors/assumptions

(1) Disability incidence rate and duration for IP
(2) Incidence rate for CI
(3) Incidence and amount for LTCI
(4) Impact of benefit size on assumptions

Question 13

Morbidity assumptions

Expand briefly on how size of benefit may impact morbidity assumptions (4)

Answer 13

For IP, CI, and most LTCI, benefit amount fixed, so no assumption needed for this

But may be correlation between incidence rates and benefit size

Only for very large policies, may insurer want to alter assumptions, to relfect better claims experience from
+PH belonging to higher socio-economic class

+stricter level of underwriting

Question 14

Morbidity rates: Disability incidence and duration for IP

Describe how these rates may be determined (4)

What factors might affect the transition intensities (5)

Describe how rates are used (2)

Describe issues surrounding estimating these rates (3)

How might we control parameter uncertainty for these rates? (3)

Answer 14

(1) Benefits for IP can be modelled using a multi-state approach

​​needs transition intensities (claim inception, recoveries, death)

calculated for homogeneous groups

+duration: recovery may differ vastly by duration in force

+disability type: recovery may dif vastly by disability type
may seperate

+second/subsequent incidences: as more likely to claim in future

(2) Intensities influenced by

+PH characteristics: identified at underwriting

+prod design features: replace ratio/rehab benefits

+economic morale: low => more likely claim

+government welfare provision

+tax: on premiums (discourage sales), relief on prems (enoucourage sales), way insurer is taxed, tax rates involved changing over time

(3) Intensities used to calculate transitions probabilities

+then construct projected numbers/proportions in each state at future ages.

+can be used to calc claim inception rates/disability annuity values

(4) Issues surrounding estimating rates

+Data limitations is the main issue

+Published insurance incidence data has limited credibility

+Worldwide stats may not be relevant

(4) Controlling parameter uncertainty

+Assuming larger risk margins

+Issuing products with review-able premiums/charges

+Reinsurance

Question 15

Morbidity rates: Incidence rate for CI

What factors influence claim distribution rates for CI (4)

What kind of factors complicate modelling/setting of assumptions (2)

Answer 15

May be necessary to estimate significant number of distributions (40+) if each condition modelled separately, plus allowance for future trends

Other influences claim distribution (other than trends), include

+advancement in medical science (cures=> more windfalls)

+diagnosing conditions earlier (more claims)

+simple/more readily available operations (more claims)

+influence new and existing business separately
new business, can adjust premiums accordingly

+existing business, can only adjust in force prems if revieawable

Factors which complicate modelling/setting assumptions

+may need to separately model claims definitions which are disease-based and/or treatment-based (eg coronary artery bypass, major organ transplant, heart valve replace)

+guaranteed and review-able alternatives

+lack of data, only cancers/heart attacks will provide enough data…otherwise hasn’t really been around long enough

Question 16

Morbidity rates: Incidence and amount for LTCI

What key assumptions do we need to estimate for LTCI? (2)

What are important factors for LTCI contract assumptions? (5)

What issues arise when estimating necessary assumptions? (3)

Answer 16

Estimate distribution of
+claim frequency
+claim amount (if funding for care)

Important influences for LTCI assumptions

(1) Medical advancements

+Transition rates: improved health may reduce inception rates and rates for people moving to higher ben-levels

+Mortality rate: improved health=> people needing benefits for longer

+Costs: changing med care may => higher costs e.g. more expensive procedeurs

(2) Economic factors

+inflation: big problem if benefits are indemnity based

+demand (for LTC) vs supply, usually demand is greater, leading to inflation heavier than economic inflation

Issues arising when estimating necessary assumptions

+Data limitations

+Little data on claim frequency to base estimates of future transition rates

+Absence of insurance statistics (industry data)

Question 17

Investment return:

List 4 factors that affect the value assigned to the investment return assumption when pricing a life insurance contract.

Answer 17

(1) Significance of assumption. This depends on:

+level of reserves (larger reserves => more important)

+extent of investment guarantees

(2) Extent of investment guarantees given under the contract. This will affect asset mix
more onerous the gaurantee => more cautious assets selected => reflected cautious investment return assumption

(3) Extent of any reinvestment risk, and extent to which reinvestment risk can be reduced by suitable asset choice: the less important reinvestment risk the less account needs to be taken of future investment yields
(4) Intended asset mix for the contract and current and likely future return

Question 18

Investment return: Market consistency

For a contract that is priced using a market-consistent approach, how do we set investment return assumption? (3)

Comment on this process specifically for stochastic modelling (2)

Comment on this process specifically for deterministic modelling (3)

Answer 18

For market consistent approach
expected investment return should be set as the risk-free rate
irrespective of the actual underlying assets held
this is true for both stochastic and deterministic models

If stochastic modelling is used
need additional assumptions for investment return volatility and correlation assumptions
which are dependent on actual underlying assets

Question 19

Non-marginal expenses + commission:

What is the general principle when setting expense/commission assumptions? (1)

How might the expense assumptions be determined? (3)

Comment on the use of an expense model (1)

Comment on how fixed expenses should be catered for (1)

Give examples of marginal expenses which may arise (8)

Answer 19

(1) Expense and commission assumptions should reflect expected expenses to be incurred in processing/subsequently administering business
(2) Assumptions would be determined by

+analysing recent experience for type of business concerned..

+…dividing expenses by function, as appropriate, and possible whether expected to be proportional to premium/benefit, or an amt per contract

+if insufficient own data? use similar other product. else industry data, else reinsurance data

(3) In practice, an expense model may constructed/used to project staff structure/associated overheads.

Output taken in conjunction with expected new business volumes to give suitable per policy/per premium costs.

Fixed expenses
Expense loadings should contain contribution for expenses not covered in marginal expense categories, but distinction between fixed/marginal sometimes blurry.

Marginal expense examples
Initial acquisition (incl commission), initial medical underwriting, initial administration, renewal administration, sales channels' renewal rewards, investment, withdrawal/PUP (usually allow for via suitable discontinuance terms), claim/maturity

Question 20

What is a key risk when setting per policy expenses? (1)

Describe 3 methods of allowing for expenses that do not vary by policy size when setting premium rates or charges (3)

Answer 20

A key risk when setting per policy expenses relates to how to incorporate expenses that do not vary by size of contract

3 methods to allow for this risk:

Individual calculation of premium rates or charges
normally only for very large cases as small cases would be very uncompetitive

Policy fee addition to premium
(or deduction from regular benefit payments) for non-linked contracts or charges that match per policy expenses for unit-linked contracts

Sum assured differential i.e. for non-linked contracts,
charge different premium rates according to which band benefit falls into and for unit-linked contracts apply different charges )(e.g. allocation rates) according to which band premium payable falls into.

Question 21

Expense inflation:

What will primarily affect the inflation assumption, and why? (2)

What 2 ‘periods’ for should be considered when setting the expense inflation assumption? (2)

List 5 factors that will considered when setting the expense inflation assumption for pricing (5)

Answer 21

Key impact on inflation will likely be earnings inflation, as insurer’s expenses are mostly staff related

Consider
+inflation between setting assumption, and point from which new policies will be sold
+inflation during term of policy

5 Factors affecting expense inflation
+Current rates of inflation, both for prices and earnings

+Expected future rates of inflation

+Difference between fixed-interest government bond yields and index-linked
government bond yields

+Recent actual experience of life insurance company or industry

+Investment assumption being used (be consistent)

Question 22

Persistency

Outline how to set the persist-ency assumption when pricing a product (7)

Answer 22

(1) persistency assumptions needed if using cashflow method, not if using formula method
(2) Reflect expected future experience of contracts to be taken out (eg full withdrawal, partial, and paid-up)
(3) Based on analysis of company’s recent experience, ideally of same contract, else of any similar contracts
(4) If company doesn’t itself have adequate data, there may be industry-wide experience it could use
(5) Assess results to see if they have been affected by special factors, e.g. adverse economic situation
(5) Adjust for differences in class of lives, e.g. benefit changes, distribution channel changes
(6) Sensitivity test/add appropriate margins

Question 23

Persistency:

What changes to benefits might lead to increased withdrawals? (6)

How might distribution channels impact withdrawals? (5)

Answer 23

Benefits

Non-linked

+Increase in discontinuance terms
+Decrease in bonuse rates

Unit-linked
+Reduced fund performance
+Increased charges
+Removal/variation of guarantees/options

Distribution channel

+Who initiates the sale: lower withdrawal if client initiates
+Different sales practice: client pressurised for sale => higher rates
+Sales without gathering proper info: mis-selling
+Financial sophistication: varies by channel=> impacts rates
+Target markets: affected by dist channel, hence PH’s affluence + level of economic wealth

Question 24

How might we allow for risk in the use of parameters in pricing? (3)

What key factors influence the margins to use? (3)

Answer 24

Parameters discussed so far would only be best estimate parameters. We can allow for risk through:

(1) through the risk element of the risk discount rate
only applicable to cashflow model

(2) using stochastic approach
only applicable to cashflow model

using best estimate for non-stochastic assumptins, using a risk free rate, modelling one/more assumption scholastically

(3) assessing margins to apply to expected values
and using a risk free rate to discount

applicable to either cashflow/formula model
formula model needs judgement, as doesn’t help actuary determine extent of risk

Use of margins depends on
degree of risk associated with each parameter used
financial significance of the risk from each parameter
purpose for assumptions
pricing => competitiveness (but also prevent losses)

Question 25

Profit requirements:

Explain what is meant by the term risk discount rate (5)

Answer 25

return on capital demanded by providers of that capital. It’s made up of:
+return they could get obtain from risk-free asset

+plus risk premium to compensate for volatility of return

+can be determined by quantifying risk premium appropriate for company e.g. using CAPM

+market availability of capital should also be taken into account

+market’s view of risk discount rate is not necessarily most apt for any given product, as different products will have different levels of riskiness.

Question 26

Profit requirements:

Deciding on a risk discount rate using statistical methods

Why can’t we simply use CAPM? (2)

What might affect the riskiness of products/projects undertaken by insurer? (6)

Answer 26

+Can’t simply use CAPM as
assumptions may not hold’

+not all projects company undertakes are equally risky (some products have more innovative features, eg)

6 things that might affect riskiness of products/project life company undertakes

\+Lack of historical data
\+High guarantees
\+Policyholder options
\+Overhead costs
\+Complexity of design
\+Untested market

Question 27

Profit requirements:

Deciding on a risk discount rate using statistical methods

How might we use a statistical approach to asses the insurer’s risks and allow for them in the RDR? (4)

Answer 27

Can assess these risks (and allow for them) by

(1) analytically, by considering variances of individual parameter values used i.e VaR[Return]
(2) sensitivity analysis
(3) using stochastic models
(4) comparison with any available market data