21 Assumptions Flashcards
A basic methodology for setting assumptions
Step 1: Investigate historical experience
- make best estimates of the parameters from that experience
- These estimates will be appropriate in the context of the historical conditions and circumstances that applied at the time of that experience
Step 2: Consider future conditions
- in the period for which you are making your assumptions.
- including the commercial and economic environment
Step 3: Determine best estimate assumption
- given expected future conditions
- historical parameters used as starting point
- but allowance made for the different circumstances of future compared to the past
Step 4: Consider the credibility and relevance of data used
- this determines the extent to which rely on experience data
- and the extent to which allow for other factors
Step 5: Add margins for prudence
- size of margin will depend on purpose of model and
- the degree of risk associated with the parameter
Obtaining best estimate assumptions for
Mortality
Consider mortality assumption in two parts:
1 - Base mortality - initial rate
* Usually based on adjustment to rates from standard table, using own mortality data for adjustments (same product or similar product)
* if own data is insufficient and there is no standard table for the product involved, then revert to industry data: CMIR, population stats or reinsurers
* Volume of data should be adequate, without introducing excessive heterogeneity due to trends over time
* Analysis: Divide data into homogenous groups subject to adequate levels of data being retained within each cell
* Additional adjustments may be necessary to reflect the expected future experience of the lives who will take out the contract being priced, which depends on:
- target market/ distribution channel
- underwriting controls applied
- expected change in experience sine the time of the last historical investigation to the point in time at which assumption will apply
2- Mortality trend - how mortality changes over time
esp important for guaranteed premium rates
Three approaches to determine future rates of mortality improvement:
1. Expectation : Expert opinion and subjective judgement to specify a range of future scenarios
2. Extrapolation - projecting historical trends
3. Explanatory - model trends in mortality from a bio-medical perspective
- deterministic projections might allow for different mortality improvement rates according to year of birth cohort
- Multi-factor predictive modelling techniques (eg using generalised linear models) combine internally held customer data (if there is sufficient volume) with external drivers, allowing for correlations and interactions between them.
- Stochastic mortality projections (Lee-Carter or P-spline method) generate many different improvement rate scenarios, but can be challenging to calibrate
Obtaining best estimate assumptions for
Morbidity
Disability incidence and duration for income protection
- modelled using a multi-state movement hierarchy
- necessary to estimate the transition intensities: claim inception, recoveries and death
- calculated for homogeneous groups
- by duration of claim or type of disability
- second and subsequent incidences will possibly need to be separated out too.
- Other influences: economic morale, government provision of welfare, and tax.
- Data limitations:published insurance parameters for incidence have limited credibility & worldwide statistics are plentiful, but may not be relevant.
Obtaining best estimate assumptions for
Morbidity
Claim incidence for critical illness products
- necessary to estimate theoretically up to forty different distributions
- each covered condition is modelled separately, plus allowance for future trends
- data: statistics provide help with historic incidence of critical illnesses (only cancer and heart attacks will have enough data)
- Other influences on claim distributions, which have different impact on new and existing business:
- Advances in medical science
- earlier diagnosis
- Simpler, more readily available operations
- complications:
1 - use of disease-based and treatment-based definitions of claims, which may need to be modelled separately.
2- guaranteed and reviewable alternatives
Obtaining best estimate assumptions for
Morbidity
Claim incidence and amount for LTCI
- estimate the distribution of claim frequency and the distribution of claim amount
- little control over the claim amount for indemnity products (unless there’s a cap)
- distribution of claim amount is dependent on the economy, inflation and capacity of long-term care facilities.
- advances in medical science and inflation of care costs influence distributions
- little data on claim frequency
- an absence of insurance statistics
Obtaining best estimate assumptions for
Investment return
Assumption is affected by:
1. signifance of assumption for profitability, which depends on level of reserves and investment guarantees given
2. Extent of investment guarantee given, which affect types of assets in which premiums will be invested
3. Extent of reinvestment risk and the extent to whci it can be reduced by suitable choice of assets.
4. The intended investment mix for the contract, current return within that mix, and the likely future return.
Market consistency:
- If a market-consistent approach is used, then the expected investment return can be set as the risk-free rate, irrespective of the actual underlying assets held for both the deterministic and stochastic approaches.
- stochastic approach requires additional assumptions: volatility and correlation which depends on underlying assets
Allowing for taxation
- allowing for appropriate rates of tax to the different components of the investment return
Allowing for future bonuses
- assuming very conservative assumptions in the premium basis: reduction in the interest rate assumption
- OR: could use more realistic assumptions but include an explicit allowance for future bonuses
Obtaining best estimate assumptions for
Expenses and commission
Parameter values should reflect the expected expenses to be incurred in processing and subsequently administering the business.
- determined after analysing the company’s recent experience for the type of business concerned
- division of the expenses by function, variable (premium&benefit) or fixed per policy
- insufficient recent experience to provide meaningful results: use data based on a similar type of business or any industry data or data from a life reinsurance company.
- parameter values for commission: to take account of the rates of commission normally paid in the market
Expense loadings:
- should cover marginal expenses and
- contribution to the company’s fixed overheads
- no loading for the administration of withdrawals or policies becoming paid-up: dealt with by discontinuance terms
Obtaining best estimate assumptions for
Dealing with per-policy expenses
expense loading per policy, but it will vary in practice in proportion to the size of the policy actually taken out.
Why? The pricing process will usually lead to a premium rate, expressed per unit of benefit
An area of risk with expenses: How to incorporate into the charging structure the expenses which do not vary by size of contract
Dealing with it:
1. Individual calculation of premium rates or charges based on the actual benefit level, age, term, etc.
2. Non-UL: Policy fee addition to the premium/ deduction from regular benefit payments
3. UL: charges that match the per-policy expenses for unit-linked contracts.
4. “Sum assured differential”. different premium rates(UL:charges) are charged according to which band the benefit (UL: premium) requested falls into
Obtaining best estimate assumptions for
Inflation of expenses
setting the value of the inflation parameter:
- current rates of inflation
- expected future rates of inflation
- differential between the return on government fixed-interest securities and on government index-linked securities,
- recent actual experience
The inflation assumption must be consistent with the future investment income assumption.
Two aspects of expense inflation:
- the inflation of expenses during the term of a future new policy
- the inflation of all expenses between “now” and the dates at which the future new policies are actually issued.
Obtaining best estimate assumptions for
Persistency (withdrawals)
The persistency (full withdrawal, partial withdrawal and paid-up rates, where applicable) assumptions should reflect the expected future experience in respect of the contracts that will be taken out.
- based on an analysis of the company’s recent experience
- should relate to the contract being priced
- if no such experience exists or the available data are inadequate, then the experience under any similar contracts would be analysed.
- industry wide experience that it could use.
- results of such analyses should be assessed to see if they have been affected by special factors such as an adverse economic situation in the country.
- If the rates are to apply to a class of lives that is expected to have a different experience from that to which the analysed data relates, then adjustments may need to be made. (due to change in benefits, target market, sales channel)
Obtaining best estimate assumptions for
Margins
Allowing for risk in cashflow model:
* through the risk element of the risk discount rate
* through using a stochastic approach
* through assessing what margins to apply to the expected values.
**Size of the margins must crucially depend on: **
* the degree of risk associated with each parameter used
* the financial significance of the risk from each parameter.
* the purpose of the basis concerned.
Obtaining best estimate assumptions for
Profit requirements
Risk discount rate
- riskier investments = investors require risk premium on return
CAPM
- proxy for risk free asset = short-term deposits issued by a stable government
- risk premium = yield on diversified portfolio of shares - RFR
- result of the CAPM is that the proper risk premium for any particular share is in proportion to its Beta.
- beta factor can be estimated by analysing the historic returns on the asset in question in conjunction with market returns
Deciding upon RDR
The higher the risk = the greater the RDR
Factors that would result in greater risk premium:
* lack of historical data
* high guarantees
* policyholder options
* overhead costs
* complexity of design
* untested market.
Rate of return = random variable R
Given a certain variance, Var [R] , R should be such that the probability of it falling below some reference level l is small
find E[R], such that P(R>rfr)=0.95, then use E[R] as RDR
Var[R] = statistical risk, which could be assessed using one of the following methods:
1. considering the variances of the individual parameter(interest, mortality, expense) values used.
2. using sensitivity analyses with deterministically assessed variations in the parameter values
3. By using stochastic models for some, or all, of the parameter values and simulation. Vary NB parameters stochastically, calculate rate of return for each run to get distribution and variance of the return
4. By using stochastic models for some, or all, of the parameter values and simulation.
How are persistency rates affected by economic deterioration
For different products
The two things to consider in a scenario of economic deterioration are
* whether people can still afford to keep the policy going, and
* whether they would get any cash from surrendering the policy.
How would change in benefits affects persistency rates?
The following would lead to increased withdrawals:
* an increase in discontinuance terms (especially surrender values), or,
* a decrease in bonus rates (or a decrease in expected bonus rates).
And for unit-linked business
* reduced fund performance (or a reduction in expected fund performance),
* an increase in charges, or
* removal/variation in options or guarantees provided.
Consistency
- The assumptions need to be considered in their totality, not in isolation.
- make realistic allowance for the way that variables behave together
- Investment return and inflation
- Tax: “I–E” type taxation then the investment income assumptions and the expense assumptions should both reflect the same tax treatment
- New business and expenses: development expenses will need to be recouped, make an appropriate contribution to the fixed expenses.
- Investment return and bonus loading: consistent in situations where bonus needs to be loaded for specifically
- Withdrawal rates and investment return: Withdrawal rates can be affected by the general economic climate
- Other products:The basis should normally be consistent with that of related products
