Chapter 12 Modelling

Question 1

Main uses of models

Answer 1

• costing & reserving for options
• model office - new business projections, embedded value, solvency, takeovers.
• reserves
• pricing - profit premium rates

Question 2

Objectives of a health insurance model

Answer 2

• 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.

Question 3

Basic features of a health insurance model

Answer 3

• 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.

Question 4

Features of Deterministic modelling process

Answer 4

• 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.

Question 5

Features of Stochastic modelling process

Answer 5

• 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.

Question 6

Why is Stochastic modelling more important for health insurance than for pure life insurance?

Answer 6

• 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)

Question 7

Choosing between Stochastic & deterministic model

Answer 7

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.

Question 8

Calibration of Stochastic models

Answer 8

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.

Question 9

What are the different sensitivities to consider?

Answer 9

• Sensitivity of model to:
• the choice of model point
• sensitivity to parameters
• when pricing
• when reserving
• when assessing return on capital/profitability

Question 10

Choice of model point sensitivity

Answer 10

• 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.

Question 11

Sensitivity of parameters

Answer 11

• 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.

Question 12

Sensitivity when pricing

Answer 12

• 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.

Question 13

Sensitivity when reserving

Answer 13

• 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

Question 14

Sensitivity when assessing RoE/profitability

Answer 14

• 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.

Question 15

Equation of value approach

Answer 15

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

Question 16

Value of claims would include?

Answer 16

• value of claims discounted for all future claims outgo over policy duration.
• Claims handling expenses
• Inflation assumptions on claims and expenses

Question 17

Value of premiums would include?

Answer 17

• 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.

Question 18

Value of expenses would include

Answer 18

• expenses not directly related to claims or premiums

- appropriate inflation will apply

Question 19

Value of investment income would include

Answer 19

• 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.

Question 20

Value of tax & other outgo would include?

Answer 20

• this can be allowed by adjsted the discount rate.

- although explicit adjustments may be made on expenses or proftit

Question 21

Value of profit to insurer would include?

Answer 21

-formula can be altered to include specific profit objective.

Question 22

Drawbacks of the formula approach

Answer 22

• 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.

Question 23

Why was Cashflow technique/approach developed?

Answer 23

• 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.

Question 24

Cashflow approach process

Answer 24

• 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.

Question 25

Typical elements of cashflow for conventional without profits business will include

Answer 25

- 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.

Question 26

Use of cashflow approach in pricing

Answer 26

- 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.

Question 27

Cashflow approach to assessing profitability process

Answer 27

- 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.

Question 28

Use of cashflow approach in assessing profitability

Answer 28

- 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

Question 29

Cashflow approach to assessing RoE

Answer 29

- 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.

Question 30

Cashflow approach to determining capital requirements

Answer 30

- 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.

Question 31

What is multi-state modelling?

Answer 31

- 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

Question 32

Multi-state modelling for pricing

Answer 32

- 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 .

Question 33

Multi-state modelling for reserving/reporting purposes

Answer 33

- 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.

Question 34

Levels of model

Answer 34

- Single policy - New business - Existing business - Full model office

Question 35

CF Basis: Profit at time T

Answer 35

Profit = Net CF + Change in reserves + Interest on reserves