Chapter 18: Rating Methodologies and Assumptions (F203 Appx. 6)

Question 1

The rating methodology used will depend on (3)

Answer 1

• CLASS of business being priced
• AVAILABILITY of relevant DATA
• MARKET in which the company is operating

Question 2

2 Components of the risk premium

Answer 2

• a PURE RISK RATE based on previous years’ experience

- a LOADING for catastrophe and/or large loss claims (which may or may not exist in the previous data)

Question 3

5 Components of the office premium

Answer 3

• a loading for the net cost of REINSURANCE
• a loading for EXPENSES including commission
• a capital charge to reflect the COST OF CAPITAL.
• INVESTMENT INCOME
• TAX

Question 4

Components of the premium:

2 “Other considerations”

Answer 4

• RATING factors

- PRACTICAL considerations concerning policy conditions, underwriting process, competition, etc.

Question 5

9 Steps involved in calculating the pure risk premium

Answer 5

• COLLECT DATA, including past exposure data and claims arising from that exposure
• ADJUST THE DATA to make it more relevant
• GROUP DATA into risk groups
• SELECT RATING MODEL or estimation process
• ANALYSE THE DATA
• SET ASSUMPTIONS required by the model or process
• TEST ASSUMPTIONS for goodness of fit or likelihood probability
• RUN THE MODEL or process to arrive at an estimate of future claim costs
• perform SENSITIVITY and SCENARIO TESTING or apply other methods, to check the validity of the assumptions

Question 6

3 Circumstances in which external data is especially useful:

Answer 6

• for a company writing a NEW OR MODIFIED CLASS of business
• where the company’s own data is sparse
• to provide confirmation of results derived from internal data.

Question 7

5 Reasons for changes in the risk

Answer 7

Because of changes in:

• the mix of underlying risk
• cover / policy conditions
• claims handling / underwriting strategy
• the method of distributions
• the level of reinsurance coverage

Question 8

4 Examples of statistical approaches used to derive a risk premium

Answer 8

• simple BURNING COST approach to premium rating, using aggregate claims data
• FREQUENCY-SEVERITY approach, where statistical distributions are fitted to the frequency and severity of claims separately and combined to give risk premium
• MULTIVARIATE MODELS, including Generalised Linear Models (GLMs)
• the “ORIGINAL LOSS CURVE” approach to premium rating

Question 9

What is mean by subdivision of data

Answer 9

Where possible and statistically relevant, we split the data into risk cells.

I.e. we subdivide the total available data into homogeneous subsets based on factors that contribute to higher or lower claims experience (eg age, gender, car, model, etc).

Question 10

Why is data subdivided

Answer 10

• Enables us to better understand the risks being handled

- Helps us to avoid cross-subsidies.

Question 11

If the experience in the ideal base period does not appear to be typical, we should (3):

Answer 11

• choose another base year that is more typical
• aggregate more years’experience or
• apply an adjustment factor to the affected base year.

Question 12

To help assess what adjustment may be needed, we could (3):

Answer 12

• gather information on the results of other insurers, to establish whether deterioration was industry-wide or specific to the insurer
• establish whether there are any global climatic or economic factors that would explain the unexpected experience
• look at previous years’ results to try to identify trends or cycles.

Question 13

4 Matters in which significant inconsistencies may arise w.r.t. historical data

Answer 13

• policy acceptance
• policy coverage
• method of distribution
• claims settlement procedures

Question 14

4 Environmental changes that might affect claims experience

Answer 14

• legislative factors
• advances in technology
• medical changes
• changes in the construction of property

Question 15

Time delays that may result in adjustments to the data may occur due to (6)

Answer 15

• time taken for sufficient claims experience to develop from the historical data
• time taken to ANALYSE the claims experience
• time taken to reach and agree the NEW PREMIUM RATES and premium structure
• time taken to administer and IMPLEMENT NEW RATES
• time delay between the risk period and the payment of claims due to REPORTING AND SETTLEMENT DELAYS
• time taken for any REGULATORY APPROVAL to introduce rates.

Question 16

2 Ways of incorporating the cost of reinsurance into a premium rate

Answer 16

• as the net cost of reinsurance (reinsurance premium less recoveries) in a premium rate based on a gross risk premium (not taking into account reinsurance recoveries), or
• as the gross cost of reinsurance (the reinsurance premium) in a premium rate based on a net risk premium (taking account of reinsurance recoveries).

Question 17

3 Stages involved in determining the required expense loadings

Answer 17

• to allocate the expenses by class or product and, possibly, by major rating factor groups
• to allocate expenses by function
• to decide on how to allow for each expense type in the rating formula

Question 18

5 Theoretical types of expenses

Answer 18

• underwriting and brokers’commission
• policy administration
• claims handling
• overheads
• levies to state insurance schemes, eg SASRIA

Question 19

3 Factors to consider when selecting an assumed rate of investment return

Answer 19

• the likely investment conditions at the time when the premiums are receivable
• the assets likely to be held (which should be matched to the nature of the liabilities)
• consistency with the inflation assumption used to project expected claims and expenses.

Question 20

Qualitative data is used when quantitative data are (4)

Answer 20

• incomplete
• inaccurate
• sparse
• where risk perception plays an important element in price determination.

Question 21

Inadequate data may distort calculations due to errors in (2)

Answer 21

• the apparent size of the business in force, and its value expressed in exposure units and premium
• the apparent claims experience and its trends, on which the projected future costs are being based

Question 22

If we adopt a deficient set of rates as a result of faulty data, the insurer might (3)

Answer 22

• suffer UNDERWRITING LOSSES if rates are too low
• suffer LOSS OF MARKET SHARE if rates are too high
• attract UNDESIRABLE RISKS, causing deterioration in underwriting experience if rates for such risks are too low.

Question 23

Discuss the initial analyses which should be conducted on the data and explain why they are done before conducting a GLM analyses for pricing with multiple rating factors.

Answer 23

• Its appropriate to check and have an understanding of the raw data that will be used in the model.
• The raw data needs to be checked for completeness.
• Check that data have not been corrupted.
• Compare the raw dta with that used in the previous review to ensure that the most recent and appropriate data are being used.
• Checks on the credibility of data in cells and homogeneity of cells should be conducted.
• Rating factors should be chosen to have as much explanatory power as possible and remove the heterogeneity within each risk group.
• Need a balance between the number of rating factors and the homogeneity of the risks.
• Good understanding of the underlying data will help when deciding on the appropriate balance of the number of factors to include in the analysis.
• To assess the validity of other risk groupings by stochastic analyses to test for differential results.
• A distribution analysis for claim amounts could be analyzed for various segments of the data. This is useful for identifying presence of large losses which may need to be addressed before fitting a GLM and also helps to better understand the statistical distribution of the claim amounts.

Question 24

Two-way analysis of variance

Answer 24

Investigate each factor and the correlations between any two of the factors.
This can explain the variability better than a one-way analysis.

A tow-way analysis may reveal that two factors are highly correlated so that only one should be included in the pricing factors.

Question 25

Modelling Considerations to take into account when setting up the GLM

Answer 25

- Sources of data and cleaning - Consider the form of GLM used before or what would be an appropriate link function - What factors to include in the model - Analysis of significance of factors - Approaches to classification - Measuring uncertainty in the estimators of the model parameters - Comparison with time - Consistency checks with other factors - Restrictions on the use of factors in the model - Correlation between predictor variables - Parameter smoothing

Question 26

Why should adjustments be made to past data when pricing.

Answer 26

- Need to ensure past experience is indicative of what might happen in the future period for which premiums are being set. - Many different factors may cause the base experience to be different from that expected during the new rating period: - -- changes in risk and/or cover - -- environmental changes - -- general trends.

Question 27

7 Examples of time delays that require adjustments to past data

Answer 27

time taken to: - DEVELOPMENT of sufficient claims experience from historical data - ANALYSE the claims experience - reach and agree the NEW PREMIUM RATES and premium structure - to administer and IMPLEMENT THE NEW RATES - between the risk period and the payment of claims due to REPORTING AND SETTLEMENT delays - for any REGULATORY APPROVAL - due to COMMUNICATION DELAYS between the insurer and reinsurer

Question 28

Change in the risk may arise because of changes in (5)

Answer 28

changes in - the mix of underlying risks - cover / policy conditions - claims handling / underwriting strategy - the level of reinsurance cover - the method of distribution

Question 29

3 Different ways claims cohorts can be grouped for run-off

Answer 29

ACCIDENT YEAR Claims are grouped according to the year in which the claim event occurred. REPORTING YEAR Claims are grouped according to the year in which they are reported to the insurer / reinsurer. UNDERWRITING YEAR Claims are grouped according to the year in which the policy covering the claim is incepted.

Question 30

Define the "pure risk premium"

Answer 30

The premium required to cover EXPECTED CLAIM AMOUNT ONLY. No allowance is made for expenses or profit. We may express it as a nominal amount, but it is usually expressed as a rate per unit of exposure.