Capital modelling methodologies

Question 1

Additional model requirements 7

Answer 1

1. All parties involved should understand the whole process
2. The model developers should understand the business deeply
3. The objectives of the model relate to an increased understanding of risk and capital by management, and decisions including the impact on risk can capital
4. There are a number of decisions that a capital model can inform
5. There is much uncertainty in the modelling process, thorough testing should be conducted to understand the extent of uncertainty and it should be communicated appropriately to those using the output of the model in decision making
6. The principle of proportionality and practicability should be considered when deciding on the level of detail to model
7. A detailed audit trail should be kept of the whole process, with special care to document the process of selecting key assumptions and other key decisions

Question 2

Additional features of a good stochastic model 5

Answer 2

1. Have all parameters clearly identified and justified
2. Be structured and documented so that it can be understood by senior management and board members who do not have actuarial expertise
3. Be capable of being run with changed parameters for sensitivity testing
4. Use a large number of simulations
5. Have a robust software platform

Question 3

Features of a good model 5

Answer 3

1. The model chosen should reflect adequately the risk profile of the classes of business being modelled
2. The parameter values used should be appropriate for the classes of business and investments being modelled
3. The outputs from the model and the degree of uncertainty surrounding them should be capable of independent verification for reasonableness and should be readily communicable to whom advice will be given
4. The model should be sufficiently detailed to deal adequately with the key risk areas and capture homogeneous classes of business, but not excessively complex so that the results become difficult to interpret and communicate or the model becomes too long or expensive to run
5. The model should be sufficiently flexible

Question 4

Methods of allocating capital 4

Answer 4

1. A percentile method - We would take the simulation which determines the capital requirement and assess how the loss in that simulation was made up
2. Marginal capital method - Here we allocate the capital with reference to the marginal capital requirements of each segment, ie we consider the additional capital that would need to be held if the element was to be added to the business (known as a “last in” method)
3. Shapley method - We allocate the capital with reference to an average of the marginal capital requirements, assuming that the class under consideration is added to the overall portfolio first, second, third etc
4. Proportions method - Allocate capital to each classes of business in proportion to its contribution to the risk metric on a standalone basis, work out the required capital separately for each line of business, and work out what proportion each of these is of the total individual capital requirements.

Question 5

Reasons for allocating the diversification benefit of capital requirements 3

Answer 5

1. Performance measurement by class, product, portfolio etc
2. Business planning and strategy setting
3. Pricing - premiums include a capital/ profit loading to reflect the cost of capital to write the business

Question 6

Factors to consider when modelling counterparty credit risk 3

Answer 6

1. Correlation between counterparties
2. Non-recoveries due to reinsurance disputes
3. Any collateral help by the insurer, which can be realised in the event of a default

Question 7

Factors to consider when modelling investment credit risk 4

Answer 7

1. The probability of default by each counterparty
2. The loss given default
3. Spread risk
4. Correlations between counterparties and between asset classes

Question 8

Factors to consider when modelling market risk 5

Answer 8

1. Changed market values of investments
2. Variation in interest rates and the effect on the market value of investments
3. Level of investment income
4. Severe economic or market downturn or upturn leading to adverse interest rate movements and/or equity market falls
5. Currency movements

Question 9

Other considerations affecting the capital impact of insurance risk: 5

Answer 9

1. Underwriting cycle
2. Parameter error
3. Multi-year policies
4. Management actions
5. Reinsurance terms in future periods

Question 10

Claims should be split into the following categories for modelling: 4

Answer 10

1. Attritional claims
2. Large claims
3. Catastrophe claims
4. Future latent claims

Question 11

Steps to building a stochastic capital model: 12

Answer 11

1. Select and appropriate model structure (which business areas to include)
2. Decide which variables to include, and their interrelationships
3. Determine the types of scenarios to develop and model
4. Collect, groups and modify the data, ie information relating tot he policies being modelled
5. Choose a suitable density function for each of the variables to be modelled stochastically
6. Estimate the parameters that should be used for each variable
7. Test and validate the reasonableness of the assumptions and their interactions
8. Ascribe values to the variables that are not being modelled stochastically
9. Construct a model based on the chosen density functions
10. Run the model many times, each time using a random sample from the chosen density functions
11. Produce a summary of results that shows the distribution of the modelled results after many simulations have been run
12. Run the model using different distributions/ parameters to check sensitivity

Question 12

Core features of capital models: 3

Answer 12

1. Risk profile
2. Risk measure
3. Risk tolerance

Question 13

What is economic capital based on: 3

Answer 13

1. The risk profile of the individual assets and liabilities in its portfolio
2. The correlation of the risks
3. The desired level of overall credit deterioration that the provider wishes to be able to withstand

Question 14

Why do insurers hold more capital than the minimum specified by regulators: 6

Answer 14

1. To reduce the risk that the available capital falls below the regulatory requirement, which would hamper the firms business activities
2. To give a greater degree of security to policyholders than implied by the relatively weak regulatory minimum
3. To maintain its credit rating
4. To meet the requirements of other stakeholders such as debt providers, whose interests may be subordinated to those of the policyholders
5. To maintain a level of working capital for investment in business development and other opportunities
6. To allow a buffer between the actual profitability of the business and the dividend stream paid to shareholders, who prefer less volatile returns

Question 15

Operational risk

Answer 15

1. Failure of admin systems or processes
2. Non-compliance
3. Fraud
4. Poor governance
5. Strategic risk
6. Failure of technology
7. Pension scheme risk
8. Major event risk