Chapter 12 - Modelling

Question 1

Main uses of modelling are: (4)

Answer 1

1. Costing and reserving for options
2. Model office - mew business projections, embedde values, solvency, takeovers
3. Reserves - statutory and management accounting
4. Pricing - profit, premium rates

Question 2

What is a model point?

Answer 2

It is a data record that is fed into the computer as input for the modelling program. It will represent either a policy or a group of policies containing data on the most important characteristics of the policy

Question 3

What factors would affect the number of model points used?

Answer 3

1. Availability and power of computers
2. Variability of contracts sold
3. Complexity of contacts in force
4. Age of the company
5. Whether the modal is stochastic or deterministic
6. The purpose and importance of the investigation
7. Time available
8. Sensitivity of the results to using more or fewer model points

Question 4

Requirements of a good model: (10)

Answer 4

1. Model used must be valid, rigorous and adequately documented
2. Model chosen should be capable of reflecting the risk profile of the financial products being modelled
3. Parameters used must allow for all features of the business being modelled
4. Inputs to the parameter values should be appropriate to business being modelled
5. Workings of the model should be easy to appreciate and communicate
6. The model should exhibit sensible joint behaviour of model variables
7. The outputs from the model should be capable of independent verification for reasonableness and should be communicable
8. Model must nit be overly complex so that either the results become difficult to interpret/communicate or the model becomes too long or expensive to run
9. The model should be capable of development and refinement
10. Range of methods of implementation should be available to facilitate testing parameterisation and focus of results

Question 5

Key features of the deterministic modelling process are as follows: (3)

Answer 5

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

Question 6

Features of a stochastic modelling process (3)

Answer 6

1. Some of the parameters in a stochastic model are allowed to vary and have their own distribution functions
2. Stochastic model st be run many times using random samples from the dsitribution functions
3. Model produces results in the form of a probability distribution

Question 7

Disadvanages of stochastic modelling (4)

Answer 7

1. Time and computing constraints
2. Outputs from model are sometimes very sensitive to (deterministically chosen) assumed values of the parameters involved
3. We may have little confidence about the probability distribution and its parameters chosen for the stochastic variables
4. Preceding two points can lead to spurious accuracy, and hence render the results of the modelling of very little practical use

Question 8

Drawbacks of formula approach: (8)

Answer 8

1. Does not allow for the proper timing of events
2. Does not allow for the accumulation of reserves
3. Does not properly allow for capital needs
4. Does not allow for the impact of net negative cashflows in any period
5. Does not allow for separate inspection of premium related cashflows or claim related cashflows
6. Does not allow easily for variation of assumptions over time
   Approach uses 1 fixed diacount rate, whereas investment returns might vary over time
7. Does not allow for changes in the assumed future experience and cannot be used to measure the sensitivity of profit to such variations
8. Can not easily allow for more complicated product structures

Question 9

Typical elements of CF for conventional without profits business will include: (8)

Answer 9

1. Premiums
2. Expenses
3. Commission
4. Claims
5. Contribution to reserves
6. Contribution to capital requirements
7. Interest on CF and reserves
8. Tax

Question 10

Additional items of CF for unit linked contracts: (8)

Answer 10

1. Cost of unit allocation
2. Bid offer spread
3. Cost of paying claims in excess of unit fund value
4. Risk charges
5. Unit charges
6. Fund management charges
7. Unit fund growth
8. Unit funds paid out on claim or surrender

Question 11

Disadvantages of writing capital intensive business: (5)

Answer 11

All other things being equal, capital intensive business will:

1. Give a lower rate of return
2. Reduce a company’s apparent financial strength (often measured sinply as free assets in relation to the reserves)
3. Increase the opportunity cost of capital, in that the company could use the same amount of capital to write more business that is less capital intensive
4. Be more exposed to risk of adverse experience, becuse it would be more diversified if it uses capital to finance a large number of non-capital intensive policies than if it uses it for a smaller number of more capital intensive policies

Question 12

Explain why multivariate modelling useful for modelling Health insurance claims?

Answer 12

Multivariate modelling using is necesaary when modelling multiple factors that are likely to be correlated to a certain extent.

Examples of factors are:
- age and family size
- age and chronic conditions
- maternity and gender

Question 13

Outline the advantages of the Tweedie distribution for modelling PMI claims data

Answer 13

• direct modelling of risk prm or incurred loss data for PMI business is problematic since a typical pure prm distribution will consist of a large spike (point mass) at zero (where policies have had no claims) and then a wide range of amounts (where policies have had claims)
• the tweedie distribution is a special member of the exponential family that has a point mass at zero and corresponds to:
  • the compound distribution of a Poisson claim number process
  • and a gamma claim size distribution

Question 14

2 properties of the exponential family of distributions which make them particularly useful when using a GLM

Answer 14

1. The distribution is completely specified in terms of its mean and variance
2. The variance of Yi (the response variable) is a function of its mean