Ch 19: Models 2

Question 1

Summary Card

Answer 1

• Pricing
• Profit criteria
• Capital & solvency
• Valuing assets and liabilities
• Dynamic solvency testing
• Sensitivity testing

Question 2

What is product pricing? (2)

Outline how models are used for product pricing (4)

Answer 2

Pricing is the process of setting the premium/charging structure, for

• new busines or
• existing business
  
  • continually monitoring validity of premium rates on exist bus
  • re-examine if expected future experience changed from that used in initial pricing)

General steps

1. Choose model points, considering
   
   1. existing bus: profile of existing bus + expected changes
   2. new bus: profile of similar bus, adj for exp future changes
2. For each MP, project cashflows, allowing for reserving + solvency capital requirements, on basis of set of assumptions
3. Discount net cashflows at RDR that allows for:
   
   • return required by company
   • level of statistical risk attaching to cashflows (so in theory, separate RDR for each component of cashflows)
   • theoretically, separate RDR used for diff CFs, since statistical risk associated with each will be different
4. Premium/charges for model point set to produce profit required by company

Question 3

Model points

What is a model point (MP)? (3)

How do model points help in the modelling exercise? (3)

Answer 3

MP is a

1. data record fed as input into a model/modelling programme…
2. …will represent either a policy or group of homogenous policies
3. …will contain most important characteristics of the policy

How model points help?

1. underlying business comprises wide range of pols
2. MPs group policies expected to produce similar results, which can then be scaled up, saving time, requiring less power
3. number of model points represent whole business

Question 4

Model points:

Choosing model points

In force business (3)

New business (3)

Answer 4

Above all, MPs chosen such as to reflect adequately the distribution of business being modelled.

In force business

1. group pols of same prod type which share acceptably similar characteristics, which will then contain average value for premiums, benefit guaranteed, etc
2. group data to fit within computer constraints
3. check validity: for block of pols=> compare grouped/ungrouped results

New business, consider

1. Look at
   
   1. new business production
   2. trends in new business pols
   3. marketing changes
   4. planned new product launches
   5. imminent legislative/fiscal changes
2. Influence on sales/persistency (for life and health care products)
   
   1. economic morale
   2. government provision of welfare
   3. tax
   4. political commitment (government offering alternatives)
3. Business volumes
4. Business mix

Question 5

Define the term ‘profit criterion’ and name 3 profit criteria (3)

Answer 5

Single figure that tries to summarise relative effeciency of contracts with different profit signatures

1. NPV (net present value)
2. IRR (internal rate of return)
3. DPP (discounted payback period)

Profit signature: seq of profits from inception to termination

Question 6

Describe the net present value criterion (2)

List 4 issues regarind the NPV criterion (4)

Answer 6

1. NPV of profit signature is calculated by discounting at risk discount rate
2. Economic theory implies NPV is best profit criterion to use. Aim to max NPV

List 4 issues with NPV criterion

1. However, it’s dependent on assumptions of
   
   1. RDR being appropriate for inherent risk
   2. operating in free and efficient capital market
2. Means little by itself (e.g. can double NPV by doubling MPs’ premiums), so NPV normally expressed in relative terms such as
   
   • in proportion to initial sales costs(comm) => implies comm in-line w/profitability
   • in proportion to total discounted premium incomes => Capture small mkt share, sell large vol on high NPV contracts focus on incr mkt share and profitability.
3. Subject to law of diminishing returns, else company could sell unlimited same policy with positive NPVs to increase profits
4. Says nothing about competitiveness: high NPV bad if can’t sell

Question 7

Define the internal rate of return profit criterion (2)

Describe the IRR (3)
State 3 reasons why the NPV may be more reliable than the IRR (3)

Answer 7

1. Defined as rate of return at which discounted value of cashflows (NVP) is zero
2. Company will usually prefer contracts with higher IRR
3. Does not always agree w/NPV => incr NPV != incr IRR

Potentially NPV may be more reliable than IRR

1. If more than one change of sign in stream of profits, IRR wil not usually be unique
2. NPV can be related to useful indicators of policy’s worth to company eg sales effort , mkt share, IRR can’t
3. NPV always exists. IRR may not exist (eg.. if policy makes profits from outset)

Question 8

Define the discounted payback (DPP) profit criterion and state why it will not usually agree with the NPV (3)
When is the DPP an important criteria? (4)

Answer 8

1. Policy duration at which the profits that have emerged so far have zero present value
2. i.e. time it takes for company to recover initial investment with interest at risk discount rate
3. DPP will not usually agree with NPV as it ignores cashflows after the DPP

When is the DPP criteria important:

1. Limited capital available=> sell policies with short DPP
2. Long term policies
3. Large initial capital strain
4. Greater variation in DPP

Question 9

Pricing: marketability of pricing results

List 5 possible responses to premiums/charges being unmarketable.

Answer 9

1. After premiums/charges that meet profit criterion have been determined, and marketability needs to be considered.
2. Reconsider product design e.g.
   
   • remove risky features
   • add product differentiating features
3. Consider distribution channel change if would cause/permit
   
   • assumption change in model
   • higher premium/charges without loss of marketability
4. Reduce company’s profit requirement
5. Decide not to market the product
6. Re-examine assumed expenses

Question 10

Pricing: capital requirements(3)

2.4.4

Answer 10

Net CFs from MPs after scaling up for New Bus will be included in model of business of whole company

1. Profitable on whole
   
   1. possible for desired profitability to be met in aggregate, and not every single MP being profitable
   2. …exposed to changes in mix of business
2. Agg profitability of product:
   
   • Look at impact on EV after any changes
   • Full model office since future new bus=> significantly affect future EV
   • project EV to allow for management action: compare EV under different management decisions
   • test outcome sensitivities to experience esp dif volumes/mix of business
3. Observe modelled CF timings and amounts
   
   1. ..to assess impact of writing new product. if capital is a problem, may need to reconsider prod design
   • new/existing bus useful
   • allow for supervisory min solvency margin

• Determine prems/charges for MP’s and interpolate for all other contract variations

Question 11

How do we go about asessing ROC (return on capital) during a pricing exercise? (3)

Answer 11

1. Gross up net cashflows for new bus, and use to assess amount of capital required to write product
   
   1. regulatory basis
   2. economic basis
2. Add one off development costs: to the extent that they have not already been amortised/included in expense CFs used
3. Total capital requirement: given by above
   
   1. can be compared with profits expected to emerge from product so as to determine expected return on capital

Question 12

Profitability: assessing existing business profitability (2)

Full policy book (2)

Representative MPs (7)

Scaling up (7)

Answer 12

1. Measurement of exp future profits
2. EV: value of fut profit stream from existing business + value of net SH assets
3. Policy by policy basis
   
   1. May use full policy data set,
   2. more accurate than MPs, but takes time/resources
4. Representative MPs
   
   1. starting point may be previous used MPs, modified for new bus, or
   2. redo MP generation based on in force bus; less prone to errors than adjusting previous MPs
   3. check MP suitability:
   4. run MPs through supervisory model and compare to published value
   5. obtain PV of projected CF using suitable RDR
   • theoretically different RDR for different CFs
   • lower RDR than on pricing as some risks reduced e.g. new business volume and mix
5. Totalling across all policies/scale MPs up
   
   1. PV of future profits: used together with NAV to get EV
   2. Proj CF’s, disc @ RDR, scale up CF’s, and agg results
   3. Check PV of profits: hopefully positive=> good financial management of product
   4. Breakdown/analysis of future profits to compare relative contr to company profile, by
      
      1. product
      2. class
      3. distribution channel
      4. subsidiaries

Question 13

What is ‘solvency’? (3)

Answer 13

Solvency

1. Solvency relates to insurer’s ability to meet future outgo, both from existing bus and from future new bus may sell
2. Enough reserves for future liabilities on existing bus + extra for anything else (cost of smoothing bonuses, new bus strain)
3. Regular solvency projections required, as part of regular supervisory submission

Question 14

Outline how an insurer should assess its capital requirements (4)

Answer 14

1. Insurer should assess amounts and types of capital needed given
   
   1. amount of liabilities
   2. types of risks inherent in those liabilities
2. Given liabilities span long period of years, necessary to project assets & liabilities into future years, allowing for:
   
   • new business plans
   • management actions e.g. changes in bonus and investment policy

Question 15

Give 2 main bases on which the values of assets and liabilities can be determined, for the purposes of measuring solvency

Answer 15

Company needs to compare assets and liabilities at point in time to assess solvency, can use following bases

1. Supervisory values
   
   • as determined for supervisory reporting
2. Economic values
   
   • based on expected future experience or using a market-consistent basis

Question 16

What is static solvency testing? (2)

List 3 disadvantages of static solvency testing (3)

Answer 16

Static solvency testing

1. Testing solvency at specific point in time
2. Won’t enable assessment of comp’s ability to withstand future changes in econ environ and particular comp’s experience

3 disadvantages of static solvency testing

1. considers only existing portfolio, no new bus
2. assumes experience for remaining duration
3. guarantees are hard to cost

Question 17

Describe the process of dynamic solvency testing (4, 10)

Answer 17

Dynamic solvency testing

1. testing solvency over future time periods
2. project revenue account/balance sheet far enough ahead to identify full effect of any potential risks
   
   1. e.g. current solvency assess shows A>L, but projecting surplus might show it runs out in few years
3. Requires full model office, with realistic representation of liability portfolio by model points
4. Projections bases either:
   
   • deterministic, using expected assumptions, with margins
   • Sens test to det effect of adverse future experience
   • stochastic (simulations), to assess probability of adverse circumstances occuring
5. take into account existing business only, or also include expected future new business

Question 18

List 5 key uses of dynamic solvency testing (5)

Answer 18

5 key uses of dynamic solvency testing

1. Managing solvency (on both supervisory and realistic bases), by assessing ability of company to withstand changes in environment
2. Setting new business plans
3. Setting investment strategy
4. Setting bonus strategy
5. Setting reinsurance strategy

Question 19

Stoch model used for dynamic solvency testing

Answer 19

• Assess prob ruin @ some future point on reg basis
• Strongest basis used
• Nested stoch models need ot be avoided
• Use approx liab.
• Only est probult ruin on a closed fund eg assess impact of mismatching on prob ruin

Question 20

Define the financial strength of a company (3, 1)

Answer 20

1. Usually refers to ability of a life company to:
   
   • withstand adverse changes in experience, including those arising from investment in higher-yielding but more volatile assets
   • fulfil its new business plans
   • meet reasonable expectations of its policyholders
2. Is often measured by level of its free assets or estate

Question 21

Define free assets (2) and the estate (1) of a life company

Answer 21

• Free assets
  
  • part of life company’s assets that are not needed to cover its liabilities
  • opinion differs as to what should be included in liabilities, and they may or may not include any solvency capital requirements
• Estate
  
  • excess of realistic value of assets over realistic value of liabilities

Question 22

List external sources of capital (4) and internal sources of capital (1) for a life company

List 7 uses of capital for life company (7)

Answer 22

Sources of capital
* Debt, equity, retained profits, Sponsors reinsurance, Gov

Uses of capital

1. Enables withstanding of adverse, often unexpected conditions
2. Enables writing of new business (covers product development costs + new business strain)
3. Enables adoption fo less restrictive investment policy
4. Smoothing surplus distributions to policyholders
5. Smoothing divident payments to shareholders
6. Reducing need for reinsurance
7. Allows seizing of profitable business opportunities (e.g. merger, takeover)

REG CUSHION

Question 23

Sensitivity testing:

Give examples of items can be sensitivity tested during an investigation? (4)

Answer 23

1. Choice of model points (MPs)
   
   1. Test adequate MPs used?
   2. Important if less than ideal set of MPs used
   3. Large # MP’s used => less prone to error.
2. Parameters
   
   1. Mis-estimation=> act exp != exp exp sens test to det range of values
   2. Sensitivity analysis to assess effect on model output of varying each parameter value, allowing for correlations
3. Testing when pricing
   
   1. Redefine product design if product overly sensitive to any factor e.g. sensitive to rising withdrawal rates=> less surr val
   2. Check model funcitionality for reasonabiliity e.g. incr withdrawal rates should reduce discounted profits
   3. Det size of margins in param values
4. Testing for business in force
   
   1. results used to assess ROC and profitability of existing bus
   2. sens analysis will enable quantification of effect of departure from chosen parameter values

Question 24

Sensitivity testing: alternative ways of allowing for risk

(2)

(4)

(4)

Answer 24

1. Statistical risk
   
   1. adjusting risk element of RDR
   2. lower RDR wiith assessment of effect on results of models of statistical risk
2. Quantify effect of departures from chosen parameter values
   
   1. assign probability distribution: allows derivation of variance of profit or ROC analytically (prob distri difficult to assign)
   2. sensitivity analysis
   3. monte carlo simulation: assess variance of profit using stochastic model for distribution of parameter
3. Stochastic model
   
   1. assess impact of options/guarantees
   2. if variable has stable/predictable probability distribution
   3. indicate effect of year on year volatility risk
   4. identify high risk future scenarios