Chapter 12 Modelling Flashcards
Main uses of models
- costing & reserving for options
- model office - new business projections, embedded value, solvency, takeovers.
- reserves
- pricing - profit premium rates
Objectives of a health insurance model
- enable an actuary working for a health insurer to give appropriate advise to run insurer in afinanially sound manner.
- used in day-to-day work of company
- provide checks & controls of business
- judgment will be required on choosing model type and selection of inputs/assumptions.
Basic features of a health insurance model
- model should allow for projection of cashflows: premiums, benefit structure, discretionary benefits, options to convert, etc.
- model should allow for cashflows arising from supervisory requirement to hold reserves & maintain adequate solvency margin.
- model should reflect cashflows from different states & transitions between states.
- model needs to allow for interactions between assets & liabilities.
- The ability to use stochastic stochastic models & simulations needs to be allowed where appropriate.
Features of Deterministic modelling process
- Each parameter has a fixed value
- The model produces a point estimate.
- It is possible to sensitivity test the results by running model and varying the parameter values.
Features of Stochastic modelling process
- Some of the parameters are allowed to vary & have their own statistical distribution.
- Stochastic model must be ran many times from random samples of the distribution functions.
- Model produces results in the form of a probability distribution.
Why is Stochastic modelling more important for health insurance than for pure life insurance?
- incidence ratio for health & care products is far less easier to predict than for pure life.
- the difficulty lies in the potential benefit amount, which may vary by policy-specified inflation(LTCI): medical inflation, (PMI),changes in accepted medical protocols (PMI)
Choosing between Stochastic & deterministic model
Stochastic model can be invaluable when:
- assessing stochastic impact of guarantees
- variable has a reasonably stably probability distribution.
- indicating the effect of year-on-year volatility on risk
- identifying potentially high-risk future scenarios
Stochastic models have their cons
- time and computing constraints
- sensitivity of results to the deterministically chosen parameter value eg mean & standard deviation a normal distribution.
Calibration of Stochastic models
different methods of setting parameters are as follows
-Risk-neutral/market-consistent calibration
-used for valuation purposes where options &
guarantees exist
-Focus here is to replicate market prices of actual
financial instruments as closely possible using an
adjusted probability measure.
-Real-world calibration
-typically used for calculating the capital to hold to
ensure solvency under extreme adverse future
scenarios.
-focus here is to use assumptions that reflect realistic
long-term expectations.
What are the different sensitivities to consider?
- Sensitivity of model to:
- the choice of model point
- sensitivity to parameters
- when pricing
- when reserving
- when assessing return on capital/profitability
Choice of model point sensitivity
- When enough nr of model points are used it isnt necessary to perform this sensitivity.
- However if less than ideal nr of model points have to be used then it is worth assessing the sensitivity of this. i.e vary the model points.
Sensitivity of parameters
- the effect of parameter mis-estimation can be assessed by varying parameter values and observing impact of model results.
- when doing this any correlation between parameters should be allowed.
Sensitivity when pricing
- allows us to assess what margins need to be incorporated into the parameter values.
- eg if current investment yield is 6% but insurer expects this to drop and produce unreasonable results then the insurer might consider dropping the yield to 4%. In order to obtain acceptable results.
- if results indicate that the product profitability is too sensitive to a certain assumption they may need to redesign product.
Sensitivity when reserving
- can be used to determine margins needed to ensure assumptions in reserves are prudent.
- can be used to assess the extent to which additional margins to reserves are needed.
- global contingency reserve might be needed to protect company from:
- asset crash
- excessive death or sickness
- mismatch between assets & liabilities
- selective exercise of policyholder options
Sensitivity when assessing RoE/profitability
- enable actuary to quantify effect of departures from chosen parameter values.
- where a distribution exists for a parameter then a variance will be produced of the profit/RoE.
- sensitivity/scenario analysis can be performed at a certain confidence intervals of the distribution.
Equation of value approach
Numerator: Value of outgo less Value of non-premium income (investment yields)
Denominator: Value of 1 unit monthly/single premium
The above values would be discounted using suitable interest rate equivalent to the return achievable by investing the proceeds of policy.
premium = numerator /denominator
Value of claims would include?
- value of claims discounted for all future claims outgo over policy duration.
- Claims handling expenses
- Inflation assumptions on claims and expenses
Value of premiums would include?
- value of 1 unit of premium income projected & discounted, allowing for escalation, persistency rates & waivers
- Expenses including commission which relate to premium size would be included here.
Value of expenses would include
- expenses not directly related to claims or premiums
- appropriate inflation will apply
Value of investment income would include
- cost of reserves ignored in this method
- it could however be included
- this value allows for timing differences between items bein received by company during the year against annual outgo, with balance invested to year-end prior to being distributed.
- rather than including an explicit cashflow for investment income we adjust the discount factors used for other cashflows.
Value of tax & other outgo would include?
- this can be allowed by adjsted the discount rate.
- although explicit adjustments may be made on expenses or proftit
Value of profit to insurer would include?
-formula can be altered to include specific profit objective.
Drawbacks of the formula approach
- considerable attraction in simplicity
- does not allow:
- for appropriate timing of events
- accumulation of reserves
- properly allow for capital needs
- impact of negative cashflows in any period
- separate inspections of premium-related or claims related cashflows.
- easily for variation of assumptions over time.
still useful for pricing short-term contracts.
Why was Cashflow technique/approach developed?
- developed to overcome drawbacks of the formula approach
- software packages handle both premium calculations & reserve setting.
- for products with options & guarantees cashflow method may be used.
Cashflow approach process
- a number of model points will be chosen to represent expected new business under product.
- in case of existing business model points will be adjusted for any expected changes in future.
-for each model point cashflows will be projected allowing for reserving, solvency capital requirements.
- the net cashflow may be investigated for the possibility of negative flows hence potential for additional reserve.
- net cashflows will then be discounted at a rate of interest, the risk discount rate.
- discount rate allows for: return required, level of statistical risk of cashflows.
- in theory discount rate should vary by cashflow.
- net cashflows will be analysed to assess the adequacy of premium to product a desired return.
- actuary may on particular model points fine-tune calcs to produce desired profits.
- or focus at an overall level without requiring every model point to be profitable.
-once acceptable premiums have been achieveed for model points, then premiums for all other contractss can be determined.
Typical elements of cashflow for conventional without profits business will include
- premiums
- expenses
- commission
- claims
- contribution to reserves
- contribution to capital requirements
- interest on cashflows
- tax
-allowance for lapses, premium holidays, benefit level changes on long-term products.
Use of cashflow approach in pricing
- PMI incurrs higher costs when sold compared to renewal costs. It may be appropriate to spread the initial cost over the expected number of renewals.
- Once a premium structure has been established for short-term policies. Cashflow projections may be used to assess the adequacy of these premiums over a longer term.
Cashflow approach to assessing profitability process
- full policy data set may be used.
- alternatively model points may be used to represent the existing book.
- the suitability of model point should be checked.
- where the assessment of profitability is at the same time as when the supervisory reserves are calculated, one check would be to use model points to determine the supervisory reserve and compare this to the published value.
- for each policy present value of cashflows should be determined using an appropriate discount rate.
- total across all policies (after scaling up) will give the expected profit from existing business.
Use of cashflow approach in assessing profitability
- it can be useful to look at profitability by: product, -product class eg short-term vs long-term, group vs individual.
- by distribution channel
- subsidiaries
- part of calculating embedded value of an insurer.
- performing this will alert the insurer if any products need to be repriced
Cashflow approach to assessing RoE
- Cashflows produced for model points can be grossed up for the expected NB and used to assess amount of capital needed to write the product. Basis can either be regulatory or economic.
- this calc can also allow for development costs which havent amortised as yet.
- this would give total capital requirement which can be compared to profits expected to emerge from products to determine expected RoE.
Cashflow approach to determining capital requirements
- net cashflows in respect of model points, scaled up for expected new business under product, will be incorporated into a model of the business as a whole (often called model office).
- the actuary can then assess the impact in capital management terms of writing the product, by observing model amount and timing of cashflows.
What is multi-state modelling?
- This is used where policyholders can exist in differenct states each with a different set of cashflows.
- This applies to LTCI in health and care insurance context.
- This applies to LTCI where a claim does not terminate the policy.
- This is a methodology where by policyholders are separately tracked through the various stages of capability and claiming as follows:
- capable premium payers
- incapacitated within deferred period
- lives becoming claimants following deferred period
- lives moving to further stages of incapacity
- lives dying
- lives recovering, reverting to premium payers
Multi-state modelling for pricing
- pricing using this approach requires proportions of lives in each state.
- the value of claims outgo depends on the nr of lives within benefit paying cohorts.
- this will be balanced against thepremium income received from those in premium paying states, plus investment income less any expenses.
- transition intensities will be applied to determine proportions in each state for the next month.
- this model could be very complex due to the nr of open states.
- however in practice cohorts/subgroups may be grouped .
Multi-state modelling for reserving/reporting purposes
- assumptions used in calculating reserves for statutory purposes may be different from those used in assessing the liabilities that are transferred on the sale of a company.
- thus assumptions used in transition intensities will vary according to the overall purpose of the analysis.
Levels of model
- Single policy
- New business
- Existing business
- Full model office
CF Basis: Profit at time T
Profit = Net CF + Change in reserves + Interest on reserves
