Chp 11 - Modelling

Question 2

List the four main uses of modelling in health and care insurance.

Answer 2

1. costing and reserving for options
2. model office – new business projections, embedded values, solvency, takeovers
3. reserves – statutory and management accounting (reserve case-estimates vs statistical estimation)
4. pricing – profit, premium rates.

Question 3

What is the prime objective in building a model?

Answer 3

1. The primary objective of building a model is to help actuaries advise insurers on maintaining sound financial management.
2. Models are used to:
   Support day-to-day operations.
   Provide checks and controls on business activities.
3. Actuarial judgement is crucial in:
   Choosing the type of model.
   Selecting input assumptions.
   Deciding on the number and type of model points (i.e., representative policyholder profiles).

Question 4

Describe the cashflows you would expect to feature in a model for projecting health insurance business.

Answer 4

1. The model must account for all potential cashflows, which depend on:
   Contract structure (premiums, benefits).
   Discretionary features (e.g., options to convert, extend, or increase cover without health evidence).
2. It should also include cashflows from supervisory requirements, such as:
   Holding reserves.
   Maintaining solvency margins.
3. The model must:
   Project cashflows separately for different states (e.g., healthy vs. disabled lives under IP insurance).
   Reflect transitions between these states.
4. Interactions between assets and liabilities must be considered, especially when both are modelled together.

Question 5

Give one reason for using stochastic modelling and simulation.

Answer 5

1. Stochastic models and simulations should be used where appropriate.
   Useful for projecting the distribution of claims outgo.
   Helps actuaries assess uncertainty and variability in future outcomes.
2. These techniques support:
   More robust financial planning.
   Better risk management for insurers

Question 6

State three key features of a deterministic process.

Answer 6

Key Features of a Deterministic Model

1. Each parameter has a fixed value.
2. The model produces a single point estimate as the result.
3. Sensitivity testing is possible by running the model with different parameter values.

Question 7

State three key features of a stochastic process.

Answer 7

Key Features of a Stochastic Model

1. Some parameters (e.g., number of claims, claim amounts) are variable and follow distribution functions.
2. The model must be run multiple times, each using a random sample from these distributions.
3. Results are produced as a probability distribution, not a single point estimate.

Question 8

Explain why, for health insurance products, the future incidence experience is far less easy to predict than for pure life insurance.

Answer 8

Challenges in Predicting Future Incidence in Health & Care Insurance

a. Less predictable than pure life insurance due to variable benefit amounts influenced by:
1. Policy-specified inflation (e.g., LTCI, IP).
2. Medical inflation (e.g., PMI).
3. Changes in accepted medical protocols (e.g., PMI).
4. Other evolving factors.

b. These uncertainties make actuarial modelling and pricing more complex and require flexible assumptions and robust forecasting techniques.

Question 9

Explain the two most common approaches to setting economic assumptions in a stochastic model.

Answer 9

Stochastic Model Calibration Methods

a. Risk-neutral (market-consistent) calibration:
1. Commonly used for valuation, especially when options and guarantees are involved.
2. Parameters are adjusted to replicate market prices of financial instruments.
3. Uses a risk-neutral probability measure.

b. Real-world calibration:
1. Typically used for future projections, such as assessing capital adequacy under adverse scenarios.
2. Assumptions reflect realistic long-term expectations.
3. Based on observable real-world probabilities and outcomes.

Question 10

Explain what is meant by a ‘sensitivity analysis’ and why one may be performed when using a model for pricing.

Answer 10

a. Impact of Model Points and Parameters on Results

1. Model results depend on:
   The choice of model points.
   The values assigned to parameters.
2. If an adequate set of model points is used:
   Testing for model point error may not be necessary.
3. If a limited or suboptimal set is used:
   The impact of different choices should be assessed.

b. Sensitivity Analysis
1. Used to investigate the effect of mis-estimated parameters.

2. Involves varying each parameter to observe changes in model output.
3. Must account for correlations between parameters.
4. Helps determine appropriate margins to include in pricing models.

Question 11

What roles could sensitivity analysis and stochastic modelling play in assessing the return on capital and profitability of the existing business of an insurance company?

Answer 11

Models for Assessing Profitability and Return on Capital

1. These models help actuaries quantify the impact of deviations from chosen parameter values.
2. When a probability distribution can be assigned to a parameter:
   It may be possible to analytically derive the variance of profit or return on capital.
   Sensitivity or scenario analysis can be performed at specific confidence intervals.
3. These analyses assist in:
   Assessing appropriate margins.
   Quantifying risks and presenting robust results to the company.

Question 12

Outline how a formula / equation-of-value approach can be used to obtain the price of a health and care insurance product.

Answer 12

a. Premium Calculation – Equation of Value

1. Core principle:
   Income must equal or exceed outgo.
   Any surplus belongs to capital providers.
2. Premium is the unknown, derived by equating:
   Forecast income with
   Forecast outgo.

b. Calculation Methodology

1. Numerator:
   Value of outgo (claims, expenses, commission, taxes, etc.)
   Minus non-premium income (e.g., investment yields)
2. Denominator:
   Value of one unit of premium (monthly, annual, or single)
3. Discounting:
   All values are discounted using a suitable interest rate.
   Rate reflects expected investment returns over the policy duration.
   Choice of rate and assumptions may vary:
   Optimistic or conservative, depending on pricing strategy.
   May include specific profit margins.
4. Final premium:
   Premium=Numerator/Denominator

Question 13

Describe the considerations that would be taken into account in valuing each of the different types of income and outgo, when using a formula method to calculate a premium.

Answer 13

a. Premium Calculation – Equation of Value

1. Core principle:
   Income must equal or exceed outgo.
   Surplus belongs to capital providers.
2. Premium is calculated as:
   Premium=(ValueofOutgo–ValueofNon-PremiumIncome)/ValueofOneUnitofPremium
   All values are discounted using a suitable interest rate.

b. Components of the Equation

1. Value of Claims
   Includes discounted future claims over the policy duration.
   Claims handling expenses are included.
   Uses standard inflation assumptions.
   Benefit escalation options (e.g., LTCI, IP) are costed separately.
2. Value of Premiums
   Projects and discounts one unit of premium income.
   Adjusts for:
   Escalation
   Persistency rates
   Premium waiver during claim
   Includes expenses linked to premium size, such as commission.
3. Value of Expenses
   Covers non-premium-related expenses.
   Projected and discounted with appropriate inflation rates.
4. Value of Investment Income
   Reflects timing differences between income and outgo.
   Ignores reserve costs (unless added for complexity).
   May use different interest adjustments for premiums vs. claims.
5. Value of Tax and Other Outgo
   Can be allowed for by:
   Adjusting the discount rate, or
   Making explicit allowances for tax impacts on expenses or profit.
6. Value of Profit to Insurer
   A specific profit margin can be targeted (e.g., 50% of annual premium).
   Incorporated by adjusting the denominator (e.g., subtracting 0.5 from the value of one unit of annual premium).

Question 14

State six disadvantages of pricing using a formula approach.

Answer 14

Limitations of the Formula Approach

1. Does not properly account for timing of events (e.g., when premiums or claims occur).
2. Ignores accumulation of reserves, which are essential for long-term solvency.
3. Fails to reflect the impact of net negative cashflows in any period.
4. Cannot separately inspect premium-related vs. claim-related cashflows.
5. Makes it difficult to:
   Vary assumptions over time.
   Assess capital needs effectively.

Question 15

Describe how a cashflow model would be used to calculate the basic pricing structure of a without-profits health insurance product. Include a list of typical components of profit included in the cashflow calculation. (Ignore considerations of capital and marketability at this stage.)

Answer 15

a. Purpose of the Model
Used to determine a premium or charging structure that meets the insurer’s profit objectives.
Applicable to both new and existing products.

b. Model Points
New business: Model points chosen to represent expected profile.
Existing business: Use current profile, adjusted for expected changes.
New products: Use similar product profiles + input from marketing teams.

c. Cashflow Projection
1. For each model point, project cashflows considering:
Reserving and solvency capital requirements
Base parameter values

2. Typical cashflow elements for conventional without-profits business:
   Premiums
   Expenses (initial, renewal, claim)
   Commission
   Claims
   Contributions to reserves
   Contributions to capital requirements
   Interest on cashflows and reserves
   Tax
3. For long-term products, also consider:
   Lapses
   Premium holidays
   Benefit level changes
   Reinsurance

d. Net Cashflow Analysis
1. Investigate for negative flows → may require additional reserves.
2. Discount net cashflows using a risk discount rate, which reflects:
Required return by the company
Statistical risk (variation around the mean)
3. Ideally, apply separate risk discount rates to each cashflow component due to differing risk levels.

e. Setting Premiums
Premiums or charges are set to achieve the desired profit.
Net cashflow analysis helps assess adequacy of premium in meeting return targets.

Question 16

Describe individual policy level and cohort level pricing.

Answer 16

1. Actuaries can focus on specific model points to refine calculations and determine appropriate premium levels.
2. Once refined, the model can be applied to other model points to generate a complete set of premiums.
3. Profitability targets can be met in aggregate, considering the expected mix and volume of new business.
4. It is not necessary for every individual model point to be profitable.
5. Policies can be grouped or banded, allowing for average assumptions to be applied across cohorts.

Question 17

Describe the risk an insurer is exposed to if certain model points are unprofitable.

Answer 17

If some model points are unprofitable, the aggregate profitability becomes sensitive to changes in the mix and volume of contracts sold.

Question 18

Describe the use of a model to assess the profitability of a life insurance company’s existing business.

Answer 18

1. To assess profitability of existing business, actuaries may:
   a. Use the full policy data set for policy-by-policy modelling.
   b. Use representative model points, possibly based on previous assessments, adjusted for:
   New business acquired.
   Business that has lapsed or matured.
2. Model point suitability should be verified:
   Especially when profitability is assessed alongside supervisory reserve calculations.
   A key check: compare modelled supervisory reserves with published values.
3. For each policy or model point:
   Present value of projected cashflows is calculated.
   Discounting is done using an appropriate risk discount rate.
4. Total expected profit from existing business is obtained by:
   Summing across all policies, or
   Scaling up model point results and then summing.

Question 19

Describe briefly how you would assess the return on capital for a new health insurance product.

Answer 19

1. Net cashflows from model points (as per Core Reading Question 14) can be:
   Grossed up for expected new business.
   Used to assess capital requirements for writing the product.
2. Capital assessment can be done on:
   A regulatory basis, or
   An economic capital basis.
3. One-off development costs should be added to capital requirements if:
   They haven’t already been amortised and included in expense cashflows.
4. This results in the total capital requirement.
5. The expected return on capital is determined by comparing:
   The total capital required, with
   The expected profits from the product.

Question 20

Briefly discuss how and why a model of the business of the whole company will be used in the process of pricing a new product.

Answer 20

1. Net cashflows from model points, scaled for expected new business, are:
   Incorporated into a company-wide model (often called a model office).
2. This allows the actuary to:
   Assess the capital management impact of writing the product.
   Do so on either a regulatory or economic capital basis.
3. By observing the amount and timing of modelled cashflows, the actuary can:
   Identify potential capital strain.
   Consider redesigning the product to reduce or adjust its financing requirements if capital is a concern.

Question 21

Describe briefly how multiple-state methodology would be used for pricing policies.

Answer 21

1. Multiple-state modelling requires:
   Determining the proportion of lives in each state using duration-based transition intensities.
2. Claims outgo is calculated as:
   Number of lives in benefit-receiving sub-cohorts × average sum insured for the month.
3. Income and expenses considered include:
   Premiums from lives in premium-paying states.
   Investment income.
   Relevant expenses and other outgoings for the month.
4. Transition intensities are applied to each status to:
   Project the distribution of lives across states for the next month.

Question 22

State the main disadvantage of using multiple-state methodology in practice, and explain how the problem is usually overcome.

Answer 22

1. In theory, multiple-state models can be highly complex, with hundreds of sub-cohorts active at any time.
2. In practice, limitations such as:
   Lack of detailed statistics to estimate all transition intensities.
   The need to avoid spurious accuracy.
3. These limitations lead to a simplified and meaningful approach, involving:
   Combining sub-cohorts.
   Reducing the number of transition intensities required.

Question 23

State why the multiple-state approach might still be useful, despite its practical problems.

Answer 23

1. Even with approximations, a multi-state model offers:
   Valuable insight into the robustness of rating and reserving structures.
   The ability to perform sensitivity testing.
2. Sensitivity testing is:
   More difficult with simpler approaches like the inception/annuity method.

Question 24

State, with examples, an important factor to a healthcare insurer in deciding whether it uses the multi-state model for a line of business.

Answer 24

1. The availability of credible data is a key factor in deciding whether to use multi-state modelling for a line of business.
2. Example applications:
   Individual income protection: Multi-state modelling is feasible due to sufficient data.
   Group income protection: May use the inception/disabled annuity approach due to insufficient data for multi-state modelling.

Question 25

State with an example how the use of multi-state modelling in reserving will differ from its use in pricing.

Answer 25

1. Similar modelling tools can be used for reserving and reporting purposes. 2. However, assumptions must be adjusted based on the purpose of the estimates. Example: Assumptions for statutory reporting reserves may differ from those used for liability assessments during a company sale. 3. Therefore, parameters like transition intensities will vary depending on the objective of the analysis.