Models

Question 1

Prime objective of models

Answer 1

To enable the actuary to provide appropriate advice, thereby enabling the company to operate in a sound financial way

Question 2

How do models achieve their prime objective?

Answer 2

1) By assisting day-to-day work of the company
2) By providing checks and controls on business

Question 3

List the different types of model

Answer 3

1) Profit test model
2) New business model
3) Existing business model
4) Full model office

Question 4

Profit test model

Answer 4

A model that projects cashflows from a single policy from issue date.

Useful for informing pricing and profit design decisions

Question 5

New business model

Answer 5

A model that projects cashflows from future sales

Useful for assessing future capital requirements for new business, and assessing overall RoC expected on future sales

Question 6

Existing business model

Answer 6

A model that projects cashflows from all the business a company has in force as at the investigation date

Useful as a means of assessing embedded value, and testing solvency of existing business

Question 7

Full model office

Answer 7

Basically a sum of a new business model and an existing business model.

A model that projects the cashflows from all business in force at the investigation date and from future expected sales

Useful for assessing the impact of future management decisions on the financial development of the company

Question 8

Requirements of models

Answer 8

Inputs:
1) The model points must represent the business accurately
2) The parameter values must be set appropriately
3) Different variables should behave realistically relative to each other

Workings:
1) The model must be valid, rigorous and adequately documented
2) The model must incorporate all material features of the business
3) The workings of the model should be easy to understand and explain
4) The model should not be overly complex

Outputs:
1) Results should be clearly displayed, verifiable and communicable to the intended recipients
2) The model should be capable of subsequent development and refinement

Question 9

Rigorous model

Answer 9

One that gives reliable and realistic (and hence useful), results under a wide range of circumstances and conditions

Question 10

List the basic features of life insurance models

Answer 10

1) Involves projecting cashflows
2) Allows for the cost of setting up supervisory reserves and required solvency margins to calculate profit flows
3) Makes proper allowance for guarantees and options
4) Allows for dynamic interactions and correlations between variables
5) Has an internal frequency of cashflow projection short enough to produce reliable results

Question 11

Sensitivity testing

Answer 11

A single deterministic result (using average assumptions) together with a series of further deterministic calculations on amended assumptions that provide upper and lower bounds on the corresponding stochastic result

Question 12

Risk discount rate

Answer 12

RDR

The rate of return required to be earned by a policy

Question 13

Model point

Answer 13

A data point that is used as input for a model. It can represent either a single policy or a group of policies. It is then sufficient for this representative single policy from each group to be run through the model, the result found and scaled up in order to give the result of the total set of policies in each group, and thus across the whole business.

Question 14

Cost of solvency margin

Answer 14

The fact that holding a solvency margin impinges on product profitability. This arises because the assets underlying the solvency margin must be invested in relatively safe assets and thus earn less than the RDR

Question 15

Deterministic model

Answer 15

A model with fixed inputs, giving a fixed output

Question 16

Stochastic model

Answer 16

A model where one or more input parameters are assigned probability distributions and outcomes are given as a likely distribution

Question 17

Advantages of stochastic models

Answer 17

1) Allows for uncertainty in parameters inputs
2) Useful for costing guarantees and options that have uncertain outcomes
3) Can explicitly include the interactions between variables, allowing such interactions to be assessed
4) Can be used to develop a likely distribution of outcomes as opposed to a single estimate
5) Can be used to estimate probabilities

Question 18

Disadvantages of stochastic models

Answer 18

1) Time constraints
2) Computing constraints
3) High sensitivity to chosen parameter estimates
4) Assigning a probability distribution to input parameters involves subjectivity and may lead to spurious accuracy

Question 19

Uses of deterministic models

Answer 19

1) With sensitivity testing, in order to get an approximation to a stochastic result with less effort
2) Where the result obtained would be very similar to, or more prudent than, a stochastically produced result
3) As an independent check to see if stochastic model results are reasonable

Question 20

Advantages of sensitivity testing

Answer 20

1) Allows one to assess the relative risk of each parameter
2) Gives an indication of what margins to incorporate
3) Allows one to assess the relative importance of each parameter
4) Allows one to compare the relative financial impact of the uncertainty associated with each parameter estimate
5) Exposes vulnerability of outcomes to unexpected future experience

Question 21

Financial economic modelling approach

Answer 21

A.K.A the market consistent approach

A modelling approach that seeks to set future unknown parameter values so as to be consistent with market values where they exist

Investment return = risk-free rate
Assets = market value
Liabilities = replicating portfolio of assets

Question 22

Risk neutral calibration of stochastic models

Answer 22

A.K.A the market-consistent calibration approach

Focuses on replicating the market prices of actual financial instruments using a risk neutral probability measure

The idea is that if the model can closely reproduce the observed values of quoted assets, then it should also be able to provide market-consistent values for unquoted asset or liability cashflows

Question 23

Real world calibration for stochastic models

Answer 23

Focuses on using assumptions which reflect realistic long-term expectations and which consequently also reflect real world probabilities and outcomes

Question 24

List the uses of models

Answer 24

CRISPPP

Capital requirements
Return on capital projection
Investment strategy development
Supervisory solvency position projection
Product pricing
Projections
Profitability of existing business

Question 25

Profit signature

Answer 25

The sequence of a contract’s profits over time from inception to termination

Question 26

Profit criterion

Answer 26

A single figure that tries to summarise the relative efficiency of contracts with different profit signatures.

By applying a profit criterion to different contracts and ranking the results, we can say with confidence which contract makes the most efficient use of a company’s capital

Question 27

Most commonly used profit criteria

Answer 27

NPV - Net Present Value
IRR - Internal Rate of Return
DPP - Discounted Payback Period

Question 28

Net Present Value

Answer 28

The discounted value of a contract’s profit signature at the risk discount rate appropriate for its level of riskiness.

Usually expressed as a proportion of
- initial sales cost
- PV of future premium income

NPV > 0 => profit-making contract

Question 29

Internal Rate of Return

Answer 29

The rate of return at which the discounted value of the future cashflows is zero.

IRR > RDR => profit-making contract

Question 30

Disadvantages of IRR as a profit criterion

Answer 30

1) It may not exist
2) Ir may not be unique
3) It may disagree with NPV in terms of ranking contracts by capital efficiency
4) It cannot be related to other indicators (such as sales cost or premium income)

Question 31

Discounted Payback Period

Answer 31

The earliest policy duration at which the profits that have emerged so far have an accumulated value of zero.

This is a useful reference for companies wishing to recoup high initial capital investment as quickly as possible.

The DPP will not usually agree with the NPV in terms of ranking contracts by capital efficiency since it ignores all cashflows post the DPP

Question 32

Describe how a cashflows model might work for few data points

Answer 32

1) For each data point, project the future cashflows (using estimated parameters and allowing for reserving and solvency margin requirements)

2) Discount those cashflows (using either:
- a RDR using best estimate parameters
- a risk-free rate using parameters that include margins for risk)

3) Calculate profit criteria

Question 33

Describe how a cashflow model might work for many heterogenous data points

Answer 33

1) For each data point, project the future cashflows (using estimated parameters and allowing for reserving and solvency margin requirements)

2) Discount those cashflows (using either:
- a RDR using best estimate parameters
- a risk-free rate using parameters that include margins for risk)

3) Calculate profit criteria

Question 34

Prices must be assessed for….

Answer 34

1) Marketability
2) Whether the company has sufficient capital to finance expected sales volume
3) Whether the RoC for the business as a whole is satisfactory

Question 35

Embedded value

Answer 35

The present value of the future profit stream from the company’s existing business

Plus

The value of any net assets separately attributable to shareholders

Can be calulated on a policy-by-policy basis or on a model points basis

Question 36

Appraisal value

Answer 36

Embedded value

Plus

Goodwill

Question 37

How do models help assess solvency?

Answer 37

Solvency is measured by comparing the value of assets to the value of liabilities on a supervisory or economic basis.

Question 38

Supervisory/regulatory basis

Answer 38

Using assumptions as determined for the purpose of supervisory reporting

Question 39

Economic/ market-consistent basis

Answer 39

Using assumptions set on the basis of expected experience of the company

Question 40

Static solvency test

Answer 40

A determination of solvency made at a particular point in time (either on a supervisory or economic basis)

Question 41

Dynamic solvency test

Answer 41

This is done using one of the above bases to project assets and liabilities to assess the company’s ability to remain solvent through future experience.

The projection may be done with a deterministic or stochastic model.

This may project only the existing business or include new business projections as well.

Question 42

List three ways of accounting for risk in a discounted cashflow model

Answer 42

1) Using a risk discount rate (risk-free rate plus a risk premium) and best estimate parameters

2) Using a risk-free rate and parameters estimates with margins for uncertainty

3) Using a stochastic model

Question 43

List three ways of dealing with a highly uncertain parameter

Answer 43

1) Try design our product to be financially insensitive to variations in the value of that parameter
2) Include higher margins in the estimate of that assumption than for other, more certain, assumptions
3) Institute other measures to change consumer behaviour

Question 44

List four ways that statistical risk [ Var(RDR) ] can be allowed for

Answer 44

1) Analytically
2) Using sensitivity analysis
3) Using stochastic modelling
4) By comparison with market data