Models Flashcards
Prime objective of models
To enable the actuary to provide appropriate advice, thereby enabling the company to operate in a sound financial way
How do models achieve their prime objective?
1) By assisting day-to-day work of the company
2) By providing checks and controls on business
List the different types of model
1) Profit test model
2) New business model
3) Existing business model
4) Full model office
Profit test model
A model that projects cashflows from a single policy from issue date.
Useful for informing pricing and profit design decisions
New business model
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
Existing business model
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
Full model office
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
Requirements of models
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
Rigorous model
One that gives reliable and realistic (and hence useful), results under a wide range of circumstances and conditions
List the basic features of life insurance models
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
Sensitivity testing
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
Risk discount rate
RDR
The rate of return required to be earned by a policy
Model point
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.
Cost of solvency margin
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
Deterministic model
A model with fixed inputs, giving a fixed output
Stochastic model
A model where one or more input parameters are assigned probability distributions and outcomes are given as a likely distribution
Advantages of stochastic models
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
Disadvantages of stochastic models
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
Uses of deterministic models
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
Advantages of sensitivity testing
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
Financial economic modelling approach
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
Risk neutral calibration of stochastic models
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
Real world calibration for stochastic models
Focuses on using assumptions which reflect realistic long-term expectations and which consequently also reflect real world probabilities and outcomes
List the uses of models
CRISPPP
Capital requirements
Return on capital projection
Investment strategy development
Supervisory solvency position projection
Product pricing
Projections
Profitability of existing business
Profit signature
The sequence of a contract’s profits over time from inception to termination
Profit criterion
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
Most commonly used profit criteria
NPV - Net Present Value
IRR - Internal Rate of Return
DPP - Discounted Payback Period
Net Present Value
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
Internal Rate of Return
The rate of return at which the discounted value of the future cashflows is zero.
IRR > RDR => profit-making contract
Disadvantages of IRR as a profit criterion
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)
Discounted Payback Period
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
Describe how a cashflows model might work for few data points
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
Describe how a cashflow model might work for many heterogenous data points
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
Prices must be assessed for….
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
Embedded value
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
Appraisal value
Embedded value
Plus
Goodwill
How do models help assess solvency?
Solvency is measured by comparing the value of assets to the value of liabilities on a supervisory or economic basis.
Supervisory/regulatory basis
Using assumptions as determined for the purpose of supervisory reporting
Economic/ market-consistent basis
Using assumptions set on the basis of expected experience of the company
Static solvency test
A determination of solvency made at a particular point in time (either on a supervisory or economic basis)
Dynamic solvency test
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.
List three ways of accounting for risk in a discounted cashflow model
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
List three ways of dealing with a highly uncertain parameter
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
List four ways that statistical risk [ Var(RDR) ] can be allowed for
1) Analytically
2) Using sensitivity analysis
3) Using stochastic modelling
4) By comparison with market data
