Chapter 18

Question 1

What are the differences between traditional and financial economic approaches to modelling

Question 2

List the requirements of models (14)

Answer 2

In general:
* avoid the impression that everything can be modelled
* A range of methods of implementation should be available to facilitate testing, parameterisation and focus of results.
Input:
* incorporate all the material features of the business
* model points must represent the business accurately
* parameter values must be set appropriately
* the model should exhibit sensible joint behaviour of model variables

The model:
* workings must be easy to explain and understand
* Valid, rigorous (provides realistic results under wide range of circumstances) for purpose and adequately documented
* model should not be too complex
* model should be capable of subsequent development and refinement

The output:
* the outputs should be capable of independent verification for reasonableness
* results should be clearly displayed, verifiable and communicable to intended recipients
* clearly state any shortcomings of the model

Question 3

List the information that a typical model point would include for a life insurance product

Answer 3

• Age
• Sex
• Term
• Coding of product type
• Sum assured
• Guarantees
• Premium
• Commission level
• Distribution channel
• # of policies
• Duration in force

Question 4

Why is difficult to estimate sales volumes for income protection business?

Answer 4

• Sales are dependent on both economic and political factors, whose impact is difficult to predict
• Most markets are quite significantly under-insured, which means that there s plenty of potential for getting the sales assumption wrong
• These are protection policies, and so will be subject to quite keen competition, especially if trying to sell to a reluctant public. Changes in the competitive position can dramatically affect sales, especially air sold through brokers
• There is the potential for mis-handling claims, which could have important repercussions on company reputation, which ca affect future sales volumes considerably

Question 5

What factors would influence the number of model points chosen? (8)

Answer 5

• the availability and power of computers
• the variability of contracts sold
• the complexity of the contracts in force
• the age of the company
• whether the model is deterministic or stochastic
• the importance of the investigation
• the time available
• the sensitivity of the results to using more or fewer model points

Question 6

Embedded value

Answer 6

This is part of the appraisal value of a proprietary life insurance company. It represents 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
Embedded value = Net assets belonging to shs + Value (future profits from existing business)

Question 7

Appraisal value

Answer 7

The appraisal value of a proprietary life insurance company is the sum of the embedded value of the company and the value to its shareholders of the future profits they expect to receive from future new business. The latter part of the appraisal value is often referred to as the “goodwill” value of the company
Appraisal value = Embedded value + Value (future profits from new business)
= Net assets + Value(future profits from existing business)+ Value (future profits from new business)
= Net assets + Value (future profits from existing business) + goodwill
= Embedded value + goodwill

Question 8

List the 4 types of models for life insurance and their uses

Answer 8

• Single policy profit test = pricing and product design
• New business model = capital requirement for new business and return on capital from future sales
• Existing business model = embedded value + solvency of existing business
• Full model office = impact of future management decisions on financial development of company (like surplus distribution, investment strategy, expense control)

Question 9

What are the basic features a life insurance model should have?

Answer 9

• it should incorporate cfs arising from the contract (for discretionary, use algorithm that references the asset share)
• make allowances for supervisory reserves and solvency requirement
• make allowance for supervisory solvency capital
• must allow for interactions
• guarantees and options
• projection frequency and time period

Question 10

Pros and cons of using a stochastic model

Answer 10

Pros:
* allows a probability disrtribution to be assigned to 1 or more unknown future parameters
* A +ve L can be calculated where a deterministic approach might otherwise produce a zero L
* the future parameters may be assumed to vary together as a dynamic set, which is particularly useful for with-profits business
* good model can provide good assessment of risks as it provides the distribution of results i.e. average, spread, tails etc.
­ * the approach is explicit about the assumptions made in modelling
Cons:
* results are sensitive to deterministically chosen assumed parameter values (garbage in garbage out)
­ * extremely complex models to build
­ * it may be difficult to derive the required assumptions
­* Run times require significant levels of computer power which may not be
available
­* Leading to the need to limit the ideal scope of the model [

Question 11

In what circumstances would a stochastic approach be preferred over a deterministic one?

Answer 11

• we need to cost guarantees and options (to avoid a zero liability)
• we need to estimate a probability
• we would wish to see the likely distribution of outcomes, not just an estimate
• the interaction between variables can be explicitly included, enabling effective assessment of interactions

Question 12

In what circumstances would a deterministic model be preferred over a stochastic one?

Answer 12

• with sensitivity testing, pin order to get an approximation to a stochastic result
• where the result obtained would be very similar(or more prudent- stress tests) to a stochastically produced result
• as a check on a stochastic model

Question 13

Alternative to stochastic model

Answer 13

Use a single deterministic result using average assumptions+ a series of further deterministic calc on amended assumptions
= upper and lower bounds on corresponding stoc result

Question 14

List ways in which a model could be inaccurate

Answer 14

• incorrect programming of product structure
• some products not modelled
• known imminent changes (fiscal regime, etc.) not allowed for
• policy options ignored
• incorrect parameter choice
• interaction of inter-dependent variables not correctly dynamic
• new business assumptions wildly optimistic or do not take account of imminent product changes or launches
• model points based on incorrect data
• misrepresentative model points
• deterministic approach where stochastic approach required
• risk discount rate does not make adequate allowance for cashflow variance
• unit of time within model too big
• miscellaneous software bugs
• misinterpretation of results by management because not communicated clearly

Question 15

Describe the common approaches to calibrating the parameters of stochastic models

Answer 15

• the risk neutral or market-consistent calibration:
  1. Choose a traded instrument
  
  • Pick a derivative or financial instrument with a known market price (e.g., an equity option, bond option, swaption).
    2. Build a stochastic model for the underlying parameters
  • Identify the variables that drive the instrument: interest rates, equity returns, volatilities, exchange rates, etc.
  • These are the stochastic parameters.
    3. Calibrate the model
  • Adjust the stochastic model parameters so that the expected present value (under risk-neutral measure) of the derivative’s cash flows matches the observed market price.
  • This ensures your model is market-consistent: it reproduces real-world traded prices.
    4. Use the calibrated model for untraded liabilities
  • Once calibrated, you now have realistic stochastic distributions for the underlying parameters.
  • Apply these same stochastic assumptions to value insurance guarantees or embedded options that don’t have a market price (like minimum maturity guarantees on unit-linked products or guaranteed annuity options).
    5. Calculate present value of liabilities
  • Simulate the payoff of each guarantee or option under your calibrated stochastic scenarios.
  • Discount appropriately to get a market-consistent valuation of your liabilities.
• The real world calibration:
• use assumptions that reflect realistic long-term expectations and which consequently reflect observable real-world probabilities and outcomes

Question 16

Profit test

Answer 16

A technique that involves discounting the future cashflows arising under a contract for assessing the expected profitability of that contract. This profitability is often used as a percentage of the first year’s premiums or commission under the contract. Profit testing can be used to determine the premium and/or the level of charges under a contract

Question 17

Estate = own fund

Answer 17

The excess of the realistic value of its assets over the realistic value of its liabilities