Chapter 12 - Modelling

Question 1

What are the 4 main types of models defined by the business they are modelling

Answer 1

• Single policy profit test model - Projects the expected cash and profit flows from a single policy from the date of issue
• New business model - This projects all the expected cash and profit flows arising from future sales of new business
• Existing business model - Projects all expected cash and profit flows arising from existing business at a particular time
• Full model office - The sum of new business model and the existing business model

Question 2

What are the main uses of models

Answer 2

• Costing and reserving options
• Model office - new business projections, embedded values, solvency, takeovers
• Reserves - statutory and management accounting
• Pricing - Profit, premium rates

Question 3

What is the prime objective of building a model

Answer 3

It is to enable the actuary to give a company appropriate advise so that it can be run in a sound financial way.

It will therefore be used to assist in the day-to-day work of the company and to provide checks and controls on its business

Question 4

What are the basic features required specifically of a health insurance model

Answer 4

SCAPI

• Needs to allow for the cashflow arising from any SUPERVISORY requirements to hold reserves and to maintain an adequate margin of solvency
• Needs to allow for all the CASHFLOWS that may arise, which will depend on the nature of the contract(s), terms of premium and benefits structure, and any discretionary benefits such as options to convert, extend or increase cover without evidence
• Need to allow for the ABILITY to use stochastic models and simulation where appropriate. Eg to simulate the possible distribution of claims outgo
• Need to PROJECT separately the cashflows arising from different states and reflect the transitions between these states. Eg. those paying a LTCI premium and those receiving benefits
• Need to allow for INTERACTIONS, especially where the assets and liabilities are modelled together

Question 5

Key features of the deterministic modelling process

Answer 5

• Each of the parameters in a deterministic model has a fixed value
• The model produces results in the form of a point estimate
• It is possible to sensitivity test the results of a deterministic model by running the model with different parameter values

Question 6

Key features of a stochastic model

Answer 6

• Some of the parameters are allowed to vary and have their own distribution functions
• A stochastic model must be run many times using random samples from the distribution functions
• The model produces the results in the form of a probability distribution

Question 7

When would you choose a stochastic model over a deterministic one

Answer 7

• When you want to assess the impact of guarantees
• When the variable of interest does have a reasonably stable and predictable probability distribution
• For indicating the effect of year-on-year volatility risk
• For identifying potentially high-risk future scenarios. Eg by tracing the sequence of events that have led to tour worst simulated outcomes

Question 8

Disadvantages of a stochastic model

Answer 8

• Time and computing constraints
• The sensitivity of the results to the assumed values (deterministically chosen) of the parameters involved

Question 9

What are the 2 types of calibration of stochastic models

Answer 9

• Risk-neutral ( market-consistent) calibration - Used for valuation purposes, particularly when there are options and guarantees. The focus of these calibrations is to replicate the market prices of actual financial instruments as closely as possible, using an adjusted (risk-neutral) probability measure.
• Real world calibration - used for projecting into the future. The focus of these calibrations is to use assumptions that reflect realistic “long-term” expectations and that consequently also reflect observable “real-world” probabilities and outcomes

Question 10

How can the mis-estimation of parameter values be investigated

Answer 10

By carrying out a sensitivity analysis - Which involves assessing the effect on the output of the model of varying each of the parameter values.

Any correlation between different parameter values should be allowed for when doing this

Question 11

How can sensitivity testing be used when reserving

Answer 11

• It can be used to assess the need for any additional risk margins, global reserves or capital requirements that may need to be set up to cover potential future adverse experience

Question 12

What are the drawback of using the formula approach to pricing

Answer 12

Does not allow for

PAISA CVC

• PROPER timing of events
• for the ACCUMULATION of reserves
• for the IMPACT of net negative cashflows in any period
• SEPARATE inspection of premium-related cashflows or claim-related cashflows
• changes in the ASSUMED future experience and cannot measure the sensitivity of profit to such variations
• CAPITAL needs
• VARIATION of assumptions over time
• COMPLICATED product structures. Eg unit-linked

Question 13

What are the typical elements of cashflow for conventional with-out profit business

Answer 13

• Premiums
• Expenses
• Commission
• Claims
• Contribution to reserves
• Contribution to capital requirements
• Interest on cashflows and reserves
• tax

Question 14

What is embedded value

Answer 14

The value of the future profit stream from the company’s existing business together with the value of any net assets separately attributable to shareholders

Question 15

What is multi-state modelling

Answer 15

This is where the policyholder can exist in different states, each state being associated with a different set of cashflows.

In Health and care insurance, this applies to LTCI, where a claim does not terminate a policy. ( so there are at least 2 states: claiming and non-claiming)

Question 16

What are the requirements of a good model

Answer 16

SCARCER FILES

Simple, but retains key features
Clear results
Adequately documented
Range of implementation methods should be available to facilitate testing
Communicable workings and output
Easy to understand
Refineable and developable

Frequency of cashflows (balance accuracy vs practicality)
Independent verification of outputs
Length of run not too long
Expense not too high
Sensible joint behavior of variables

Question 17

Outline the operational issues that need to be considered when designing and constructing a model

Answer 17

SCARCER FILES

Simple, but retains key features
Clear results
Adequately documented
Range of implementation methods should be available to facilitate testing
Communicable workings and output
Easy to understand
Refineable and developable

Frequency of cashflows (balance accuracy vs practicality)
Independent verification of outputs
Length of run not too long
Expense not too high
Sensible joint behavior of variables

Question 18

What are the relative merits of deterministic vs stochastic models?

Answer 18

Deterministic:
- Quicker, cheaper and easier to design, build and run
- Clearer what scenarios have been tested
- Results are easier to explain to a non-technical audience

Stochastic:
GATE I

• Good at identifying extreme outcomes, which may not have been thought of under a deterministic scenario
• Allows naturally for the uncertainty of outcomes
• Test a wider range of scenarios
• Enable better modelling of the correlations between variables
• Important in assessing the impact of financial guarantees

Question 19

Cashflow approach to pricing

Answer 19

Many Elephants Prefer Apples, It’s Definitely A Favorite Until Pears Disappear

• Choose MODEL points to represent expected new business.
• For an EXISITING product, modify the profile of the existing business to obtain the model points; for a new product, use the profile of any similar existing product with advice from the marketing department.
• PROJECT cashflows for each model point, including typical elements of cashflow (e.g., premiums, expenses, claims)
• ALLOWANCE could be made for lapses, premium holidays, reinsurance, etc for long term products
• INVESTIGATE net cashflows for negative flows and the need for additional reserves.
• DISCOUNT net projected cashflows at a risk discount rate.
• ANALYSE the net cashflow to assess the adequacy of the premium in producing the desired return.
• FINE-tune calculations for required premium levels by focusing on particular model points.
• If certain model points are UNPROFITABLE, aggregate profitability is exposed to changes in mix and volumes of contracts sold.
• PERFORM sensitivity tests by varying assumptions.
• DETERMINE acceptable premiums for model points, then use them to determine premiums for all contract variations

Question 20

Cashflow approach to profitability

Answer 20

Fishing may require some patience, especially during tough-times

• The FULL policy data set can be used to model individual policies.
• Alternatively, MODEL points can represent the business. Previous assessments may form a starting point for the model points, with adjustments for new business and business going off the books.
• It is common to REDO the model generation process based on the current policy portfolio.
• Check the SUITABILITY of any model points used.
• To check the PROFITABILITY of the business, use model points to determine supervisory reserves and compare with the published value.
• For EACH policy or model point, obtain the present value of projected cashflows using the cashflow approach to pricing.
• DISCOUNT cashflows using an appropriate risk discount rate.
• TOTAL the present value of projected cashflows across all policies or scale up the results of each model point to determine the expected profit from the existing business

Question 21

What is spurious accuracy

Answer 21

It is when the results of the model depend heavily on the parameters that have little credibility