12. Modelling

Question 1

Uses of models

Answer 1

• costing and reserving options
• model office - new business projections, EV, solvency takeover
• reserves - statutory and management accounting
• pricing - profit, premium rates
• product design
• AoS exercises
• determining capital requirements
• ALM (setting investment strategy)
• expense budgeting
• assess reinsurance needs and how to satisfy them

Question 2

Requirements of a good model

Answer 2

• valid, rigorous, adequately documented
• capable of reflecting risk profile of financial products modelled
• parameters allow for all features of business being modelled
• sensible joint behaviour of variables
• workings communicable
• outputs capable of independent verification for reasonableness
• not overly complex such that results become difficult to interpret / expensive to run
• capable of development and refinement

Question 3

Deterministic and stochastic modelling

Answer 3

Deterministic
- each parameters have fixed value
- produce results in form of point estimate
- possible to sensitivity test by running model with different parameter values

Stochastic
- some parameters allowed to vary and have their own distribution functions
- run many times using random samples from the distribution function
- products results in the form of a probability distribution

Question 4

Stochastic model invaluable

Answer 4

• trying to assess impact of guarantees
• variable of interest does not have a reasonable and stable predictable probability distribution
• indicating the effect of year-on-year volatility
• identifying high-risk future scenarios

Disadvantages
- time and computing constraints
- sensitivity of results to deterministically assumed values of the parameters involved

Question 5

Sensitivity testing

Answer 5

• assessing the effect of the model varying each of the parameter values
• allows to compare the relative financial impact of the uncertainty associated with each parameter estimate
• ## if a particular estimate is highly uncertain, we would try to design the product to be financially insensitive as possible to variations in that parameter

Question 6

Formula approach to pricing

Answer 6

• a formula approach to pricing uses an equation of value
• income and outgo are discounted by rate of return expected on future investment
• may be an explicit allowance for profit
• disadvantages, does not allow for: proper timing of events, accumulation of reserves, capital needs, variations in assumptions over time, capital needs,

Question 7

Cashflow techniques

Answer 7

Process
- model points chosen to reflect expected new business
- existing product - profile of existing business, modified to allow for changes in future can be used to obtain model points
- for each model point, cashflows will be projected, allowing for reserving and SCR
- for long-term products allowance should be made for lapses, premium holidays, benefit level changes etc.
- net cashflow may be investigated for possibility of negative flows, and hence potential need for additional reserves
- net projected CF discounted at risk discount rate accounting for: return required by company, level of statistical risk attaching to the cashflows under the particular product
- the premium for the model point can then be set to produce the required profti
- possible for desired aggregate profitability to be reached, without having each model point being profitable in its own right

Question 8

Cashflow approach can be used to

Answer 8

• price long-term contracts
• assess profitability of existing business
• determine expected return on capital for a product (ROC)
• assess capital requirements of writing new business