Ch 19: Models (2)

Question 1

Different types of model

Answer 1

• Profit test model
• New business model
• Existing business model
• Full model office

Question 2

Actuary advising a life insurer will require models to assist with:

Answer 2

• Product pricing
• Assessing return on capital
• Assessing capital requirements
• Assessing the profitability of existing business
• Developing an appropriate investment strategy
• Projecting future supervisory solvency position

Question 3

Pricing model procedure:

Answer 3

• Model can be used to determine a premium or charging structure for new or existing products that will meet the profit requirement
• Continious monitoring of the validity of premium rates on existing business is required (if expected future xp is different from when the premiums were set)
• Model points chosen:
  * Existing product - profile of existing business adjusted for any expected changes in future xp
  * New product - profile of similar existing product combined with advice from marketing department
• For each model point cashflows will be projected allowing for reserving and solvency margin reqs on the basis of a set of base values for the parameters in the model.
• Net projected cashflows will then be discounted at risk discount rate (allows for required return and risk associated with the cashflows)
• The premium or charges are then set as to produce the profit required by the company. based on the profit criterion
• Other pricing considerations must be considered for
• Essential that all prices are sensitivity tested
• Once acceptable premiums/charges have been determined for all the model points, premiums/charges can be determined for all product variations (interpolation)

Question 4

Profit criterions: (def and options)

Answer 4

• Single figure that tries to summarise the relative efficiency of contracts with different profit signatures
• Options:
  * NPV
  * IRR
  * Discounted payback period

Question 5

Considerations when using NPV as profit criterion

Answer 5

• Depends on assumptions including:
  * Market is perfectly free and efficient
  * When two risky investments are compared each is discounted at a risk discount rate appropriate to its riskiness
• It is subject to the law of diminishing returns (if it were not then a policy with positive NPV could be sold without limit)
• It does not consider competition - designing a contract with high NPV is easy, but can it be sold?
• To compare different product designs, it is necessary to find some measuring standard for meaningful comparison (% of PV of premiums) - market share captured

Question 6

Internal rate of return def

Answer 6

Defined as the rate of return at which the discounted value of cashflows is zero. All else being equal, company should prefer the product with higher IRR. Doed not always agree with NPV.

Question 7

NPV may be more reliable than IRR in some cases:

Answer 7

• If more than one change in sign in stream of profits then IRR may not be unique
• NPV can be related to effort in sale or market share while IRR cannot
• If a policy makes a profit from outset, the IRR may not exist.

Question 8

Discounted payback period def:

Answer 8

It is the policy duration at which the profits which have emerged so far have present value zero, i.e. time it takes to recover initial investment with interest at the risk discount rate

Question 9

Other pricing considerations (3)

Answer 9

• Marketability (may lead to reconsideration of:)
  * design of product - remove risky features or include differentiating features)
  * Distribution channel used - could permit other assumptions to be used in pricing or higher premiums/charges could be charged without loss of marketability.
  * Company’s profit requirement
  * Whether to proceed with marketing the product.
• Whether company has sufficient capital to finance expected sales volume - may lead to reconsideration of the prodct design as to reduce or amend the timing of the financing req
• Whether the return on capital for the business as a whole is satisfactory

Question 10

Need for capital (7) and (1) on too much capital

Answer 10

• to withstand adverse, unexpected conditions
• write new business (meet development costs of new coontracts, and fund the capital requirements that arise from writing new business)
• Adopt a less restrictive investment policy so as to meet the investment aim sof the company
• Smooth surplus distributions
• Reduce need for reinsurance
• Smooth dividend payments to shareholders
• Allow company to seize on any profitable business opportunities as they present themselves
• Too much capital could result in cash drain where it will earn less than the risk discount rate meaning that other capital will have to earn more than the risk discount rate in order to give a total return of at least the required risk discount rate.

Question 11

Sensitivity of model to model point selection

Answer 11

• If an adequate set of model points has been chosen, not necessary to test for the effect of model point error
• Possible that less than ideal model points has to be used in which case the effect on a different choice should be assessed

Question 12

Sensitivity to parameters and sensitivity analysis (3)

Answer 12

• Effect of mis-estimation of parameter values can be investigated through sensitivity analysis
• Involves assessing the effect on the output of the model of varying each of the parameter values - should allow for correlations between different parameters.
• Will help to assess what margins need to be incorporated into the parameter values or what product design features could be changed to reflect the higher risk or to make the product less sensitive to that parameter
• In some cases better than stochastic analysis since no subjectivity in deciding on the probability distributions.