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.