Chapter 22: Capital Modelling Methodologies

Question 1

The aim of a capital model

Answer 1

Can be used to help the insurance company determine the LEVEL OF CAPITAL TO HOLD.

The model will also enable the company to better understand their risks and inform business decisions.

Question 2

Available capital

Answer 2

The excess of an insurer’s financial assets over the value of their liabilities.

Question 3

Required capital

Answer 3

The amount of capital an insurer needs to set aside to allow the insurer to withstand losses.

Question 4

2 Main types of required capital

Answer 4

• regulatory capital

- economic capital

Question 5

Regulatory capital

Answer 5

(a.k.a. solvency capital)

An amount of capital an insurer is required to hold for regulatory purposes.

Question 6

Economic capital

Answer 6

An amount of capital that a provider determines is appropriate to hold given its assets, its liabilities and its business objectives.
This will be higher than the minimum regulatory capital.

Question 7

Why might an insurer hold more capital than the minimum specified by regulators? (6)

Answer 7

• to reduce the risk that avilable capital falls below the regulatory requirement, (which would hamper the firm’s business activities).
• greater degree of SECURITY TO POLICYHOLDERS
• to maintain its CREDIT RATING
• to meet other STAKEHOLDER REQUIREMENTS, such as debt providers (or subordinated debtholders, in which the regulator has no interest).
• to mainain a level of WORKING CAPITAL for investment in business development and other opportunities
• to allow a buffer between the actual profitability of the business and the dividend stream paid to shareholders (who prefer less volatile returns).

Question 8

Economic capital will typically be determined based upon (3)

Answer 8

RISK-BASED CAPITAL ASSESSMENT:

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

Question 9

internal model

Answer 9

a capital model developed internally specifically to measure the insurer’s risks.
It is commonly used to determine the amount of economic capital required.

Question 10

Economic balance sheet (3)

Answer 10

Used to assess the level of available capital.

It shows

• the market value of a provider’s assets (MVA)
• the market value of a provider’s liabilities (MVL)
• the provider’s available capital, MVA - MVL

Question 11

A risk profile is fundamentally defined by (2)

Answer 11

• the risks that have been modelled (and the way in which they have been modelled)
• the key outcome used to measure success or failure

Question 12

Risk measure

Answer 12

The risk measure links the outcome (such as avoiding a balance sheet deficit) to the capital required to achieve that outcome.

The risk measure will be defined in terms of a required confidence level and time horizon.

Question 13

Risk tolerance

Answer 13

The required confidence level stated in the risk measure.

It is simply a parameter (or set of parameters) that links the risk measure, as applied to the risk profile, to a single capital amount.

Question 14

6 Common risk categories in a capital model

Answer 14

• insurance risk
• market risk
• credit risk
• operational risk
• group risk
• liquidity risk

Question 15

Insurance risk

Answer 15

The risk of loss arising from the inherent uncertainties about the occurrence, amount and timing of insurance liabilities, expenses and premiums.

Question 16

2 Components of insurance risks

Answer 16

• underwriting risk, (relating to risks yet to be written / earned)
• reserving risk (relating to risks already earned)

Question 17

3 Risks included under underwriting risk

Answer 17

• claims higher than expected
• premium volumes lower than expected
• expenses higher than expected eg related to mix of business

Question 18

Reserving risk

Answer 18

will cover the risk that claims and/or expenses on expired business turn out to be HIGHER THAN THE RESERVES held.

This may be from:

• underestimating development on notified claims (IBNER)
• underestimating IBNR

Question 19

Market risk

Answer 19

The risk that, as a result of market movements, a firm may be exposed to fluctuations in the value of its assets or in the level of income from its assets.

The risk exists to the extent that any movement in assets is not matched by a corresponding movement in the liabilities.

Question 20

Market risk can be divided into (3)

Answer 20

• the consequences of changes in asset values
• the consequent changes in the value of the liabilities, if these are valued on a mark-to-market basis
• the consequences of a provider not matching asset and liability cashflows

Question 21

4 sources of general market risk

Answer 21

movements in:

• interest rates
• exchange rates
• equity prices
• real estate prices

Question 22

Credit risk

Answer 22

The risk of financial loss due to another party failing to meet its obligations, or failing to do so in a timely fashion.

Question 23

2 categories of credit risk

Answer 23

• investment credit risk, e.g. from holdings of non-government bonds
• counterparty credit risk, namely reinsurance recoverables, and where material, premium debtors, including pipeline premiums, and other balances with intermediaries and banks.e

Question 24

Operational risk

Answer 24

the risk of loss resulting from inadequate or failed internal processses, people or systems or from external events.

Question 25

Group risk

Answer 25

the risk a firm experiences from being part of a group as opposed to being a standalone entity.

Question 26

Liqudity risk

Answer 26

The risk that a firm is unable to meet its obligations as they fall due as a consequence of having a timing mismatch or a mismatch between assets and liabilities.

Question 27

Stochastic model

Answer 27

One in which we assume some of the variables in the business plan have an underlying probability distribution.

This enables us to describe critical assumptions, and their financial implications, in terms of ranges of possible outcomes.

Question 28

9 Stages in building a stochastic model

Answer 28

• select an appropriate model structure
• decide which variables to include, and their interrelationships.
• determine the types of scenarios to develop and model.
• collect group and modify the data,
• choose a suitable density function for each of the stochastic variables
• estimate the parameters that should be used for each variable.
• test and validate the reasonableness of the assumptions and their interactions. If the goodness of fit is not acceptable, then attempt to fit a different density function(s).
• ascribe values to the deterministic variables
• construct a model based on the chosen density functions.

Question 29

Running a stochastic model (3)

Answer 29

Once the model has been built,

• run the model many times, each time using a random sample from the chosen density function(s). The constructed model then calculates the net profit based on the values simulated from each pdf in the model.
• produce a summary of results that shows the distribution of the modelled results after many simulations have been run.
• run the model using different distributions / parameters to check sensitivity.

Question 30

3 Advantages of stochastic model

Answer 30

• test a WIDER RANGE OF SCENARIOS
• we can derive a PROBABILITY DISTRIBUTION OF OUTCOMES
• A stochastic approach explores all possible combination of stresses and can rank these against the chosen risk measure.

Question 31

9 Advantages of deterministic models

Answer 31

• the model is usually easier to design and quicker to run
• we can introduce more detail and ensure use an intelligent selection of scenarios
• we can often make the results more comprehensible (understandable)
• Deterministic models are more readily explicable to a non-technical audience.
• By developing stresses and scenarios we can help link the capital model with the risk register, helping to integrate capital and risk management
• It is clearer which economic scenarios have been tested.
• It is important to consider potential cause and effect relationship between risks.
• Even where we have used a stochastic model, stress tests using a deterministic model are useful to check / validate the model for reasonableness and to calibrate assumptions.

Question 32

4 Categories of claims that should be analysed separetly

Answer 32

• attritional claims
• large claims
• catastrophe claims
• future latent claims

Question 33

How are future latent claims modelled?

Answer 33

Insurers are unlikely to be able to model future latent claims based on past experience.
Instead a more approximate approach such as a subjective loading is likely to be used.

Question 34

The capital impact of the reserving risk

Answer 34

The difference between:

• the eventual cost at the firm’s chosen level of risk tolerance of settling claims for the business written / earned before the modelled period
• the current reserves held for those claims

Question 35

5 Factors to consider when modelling market risk

Answer 35

• changed market values of investments
• variation in interest rates and the effect on the market value of investments
• level of investment income
• severe economic or market downturn or upturn leading to adverse interest rate movements and/or equity market falls
• currency movements

The effect of each of these factors on liabilities should also be considered, so that the market risk on the net solvency position can be assessed.

Question 36

3 approaches to model market risks and model assets

Answer 36

• model each asset individually
• group similar assets, or
• model a notional portfolio

Question 37

2 Methods of modelling market risk

Answer 37

• simple stress testing

- using an economic scenario generator

Question 38

In designing suitable scenarios, we should consider (2)

Answer 38

• potential “ripple” effects, e.g., overlaps between adverse economic or insurance scenarios and the behaviour of counterparties
• hidden costs of adverse credit scenarios; e.g., extra costs of collection, or delays contributing to liquidity risk and reducing the present value of recoveries.

Question 39

5 examples of stress tests

Answer 39

• failure of the largest reinsurer
• any existing or possible future disputes relating to reinsurance contracts on a pessimistic basis that are not reflected in the value attributed to the reinsurances
• failure of the largest intermediary
• one not downgrade of all reinsurers and the impact on the output of a stochastic model if rating inputs were changed
• default of the most significant corporate investment

Question 40

5 Types of correlation to allow for in our models

Answer 40

Correlation between the following categories:

• Underwriting classes of business (e.g. motor and household)
• Risk Types (e.g. underwriting risk and reserving risk)
• Successive years (one year correlated with the previous)
• Legal entities within a group

Question 41

Allocating the total capital held between classes, products or individual policies may be necessary for (3)

Answer 41

• performance measurement (to accurately assess the profit as a percentage of capital required)
• business planning and strategy setting
• pricing (Premiums include a capital / profit loading reflecting the cost of capital)

Question 42

4 Methods of allocating capital

Answer 42

• a percentile method
• a marginal percentile capital method
• the Shapley method
• a proportions method

Question 43

Capital allocation:

Percentile method

Answer 43

This method is applied to the output of a stochastic model.
We would take the simulation which determines the capital requirement and assess how the loss in that simulation was made up.
E.g., if we ran 10 000 simulations, the simulation giving the 50th worst results (1 in 200 loss) would be analysed to assess what the underwriting result was in each class, what the investment return was, etc.

In practice the insurer may look at a number of simulations on either side of this (to reduce randomness).

Question 44

Marginal capital method

Answer 44

We allocate capital with reference to the marginal capital requirements of each segments.
I.e. we consider the additional capital that would need to be held if the element was to be added to the business.

Question 45

Shapley method

Answer 45

An extension to the marginal capital method, based on game theory.

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, …

I.e. for any one class of business, calculate each capital amount that would be required if we add the class to the overall portfolio first, second, third, etc.
We then take the ACTUAL CAPITAL REQUIREMENT AS THE AVERAGE of these amounts

The advantage is that the allocated capital is NOT DEPENDENT ON THE ORDER in which it was allocated to each class.

Question 46

Proportions Method

Answer 46

May also allocate economic capital to each class of business in proportion to its contribution to the risk metric on a standalone basis.

We would first calculate the required capital separately for each line of business, and work out what proportion of each of these is of the total of the individual capital requirements.

We then calculate the aggregate capital requirement, allowing for any diversification benefits, and allocate this to each class, according to the proportions calculated.

Question 47

3 Types of capital to allocate

Answer 47

• Total capital
• Economic capital
• Excess capital

Note: Total capital = economic capital + excess capital

Question 48

2 Uses of data in a capital model

Answer 48

• to create the model of the business as at the run date of the capital model
• as inputs to selecting assumptions used to simulate the firms results and capital over the period covered by the capital model

Question 49

14 Main items of data needed to crease the model of the business

Answer 49

• Gross and net of reinsurance unexpired premiums at the as at date of the capital model, by class of business
• Gross and net of reinsurance premium planned to be written over the new business period to be covered by the model, by class of business.
• Gross unpaid claims at the as at date of the capital model, by class of business.
• Claims payment profiles (that is, sizes, frequencies and settlement patterns)
• Policy limits, and the likelihood of claims reaching such limits
• The costs of future reinsurance
• The reinsurance programmes to which gross unpaid claims are subject, each reinsurer’s participation on the programme and the extent to which claims paid have used up coverage available on these programmes.
• The total reinsurers’ share of unpaid claims with, to the extent that it can be ascertained, each reinsurer’s share of the total.
• The reinsurance programme to which claims arising from unexpired business is subject. If the actual programme at the time of carrying out the modelling is not known, a planned programme is needed.
• The planned reinsurance programme to which claims arising from unexpired business is subject. If the actual programme at the time of carrying out the modelling is not known, a planned programme is needed.
• The planned reinsurance programme to which claims covered by the model are subject.
• The expenses of the firm.
• The value of the assets by asset category
• Credit exposures; e.g. broker balances
• Details of operational risks - normally identified in a risk map.

Question 50

14 Possible assumptions used in capital modelling

Answer 50

• Gross written premium
• Ceded premiums, including premium to reinstatement reinsurance and purchases of any reinsurance on a “losses occurring during” basis needed to cover claims occurring after the capital model date arising from business written prior to the capital model date
• Ultimate gross claims by class of business, split by attritional, large and catastrophe claims
• Claims payment profiles
• Gross reserve movements, by class of business
• Reinsurers’ share of gross ultimate claims
• The proportion of reinsurers’ share of gross claims that the firm is unable to recover, by reinsurer
• Reinsurance exhaustion
• Reinsurer downgrade assumptions (possible changes in default risk)
• Expenses, acquisition and administration
• Inflation and investment returns by asset class
• Operational losses
• Tax and dividends
• Relationships / correlations between different components of the model

Question 51

5 Features of a good model

Answer 51

• adequately reflects the risk profile of the classes of business being modelled.
• parameter values used should be appropriate for the classes of business, and investments being modelled.
• 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.
• 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.
• The model should be sufficiently flexible. The model should be capable of development and refinement - nothing complex can be successfully designed and built in a single attempt. In addition, a range of methods of implementation should be available to facilitate testing, parameterisation and focus of results.

Question 52

5 Additional features of a good STOCHASTIC mdoel

Answer 52

A good stochastic model should:

• have all parameters clearly identified and justified
• be structured and documented so that it can be understood by senior managemend and board members who do not have actuarial expertise.
• be capable of being run with changed parameters for sensitivity testing.
• use a large number of simulations
• have a robust software platform.

Question 53

3 Key objectives of any capital requirement regime

Answer 53

To ensure that:

Senior management focus on risk management - a risk management framework should be central to this process.

There is a link between risk and capital setting - in making an assessment of capital adequacy, a firm should:

• identify the significant risks facing the business
• assess their impact (both prior to and post having controls in place)
• quantify how much capital is required

The capital model is being used within the decision making process - we demonstrate this through clear documentation of all prudential risks, processes and controls.

Question 54

How might a capital model be used to inform management decision making in:
reinsurance

Answer 54

optimising the purchase of reinsurance - this may involve deciding on the retention level that optimises the savings in reinsurance premiums and the capital required.

Question 55

How might a capital model be used to inform management decision making in:
investment

Answer 55

assessing the impact of a change in the investment mix on the capital required and expected return.

Question 56

How might a capital model be used to inform management decision making in:
pricing

Answer 56

assessing return on capital for pricing and performance measurement

Question 57

How might a capital model be used to inform management decision making in:
reserving

Answer 57

quantifying the uncertainty in claims reserves - the capital model may be used to give a range of outcomes around a deterministic best estimate.

Question 58

How might a capital model be used to inform management decision making in:
strategy

Answer 58

assessing the risks and diversification benefit of new strategies, eg assessing the capital implications of a proposed new class to determine taking account of any diversification benefits and comparing this to the expected return on the class.

Question 59

How might a capital model be used to inform management decision making in:
risk management

Answer 59

identifying key risks based on the model output and assessing the impact of mitigation.

Question 60

Claims characteristics

Answer 60

Refer to the ways and speeds with which claims

• originate
• are notified
• are settled and paid
• and reopened.

Claim frequency and amount, as well as potential accumulations are relevant.

Question 61

How are attritional claims modelled?

Answer 61

AGGREGATE DISTRIBUTION using a Lognormal/similar.

• Due to the high number of losses classified as attritional, the stability of the distribution means that the aggregate distribution is appropriate.
• The loss distribution can also be linked to premium income.

Question 62

How are large losses modelled?

Answer 62

FREQUENCY-SEVERITY
allows more details of the available information to be used, expecially important where there is scarce data.

FREQUENCY ~ Poisson/Negative Binomial

SEVERITY ~ Pareto/LogNormal or other heavy-tailed distribution.

• The additional detail is worth the effort due to the larger values and will enable reinsurance limits to be tested more adequately.
• Need to decide on a threshold per class of business above which large losses will be modelled.

Question 63

How will catastrophe losses be modelled?

Answer 63

• Catastrophe losses will be modelled using different approaches depending on the peril.

Earthquake: may use catastrophe model which applies losses to the exposure base.
Factors which will affect the size of the loss include event magnitued and location.

Other perils such as hail/flood etc. may be modelled using a frequency-severity approach.

This could be based on historic losses experienced by the insurer/industry or purely a theoretical forecast model.

Question 64

Reasons why capital allocation is desirable:

Performance measurement

Answer 64

Capital has a cost. Therefore to accurately assess the performance of a particular class we need to calculate the profit/return as a percentage of the capital required to write that class, i.e. return on equity.
This requires knowing the capital cost for each class.

Question 65

Reasons why capital allocation is desirable:

Business planning and strategy setting

Answer 65

If the insurer can allocate capital to different areas of the business (and hence understand risk adjusted performance) then it can make decisions about which areas of the business to develop based on return and capital.

Question 66

Reasons why capital allocation is desirable:

Pricing

Answer 66

Premiums charged should have a capital/profit loading to reflect the cost of capital held to write the business. Any pricing exercise should allow for diversification benefits between policies, which results in the total capital requirement being lower. This allows the insurer to charge more competitive premiums. The insurer will thus want to allocate capital to products or even policies so that premium rates can accurately take account of the risk of the product/policy.

Question 67

Describe the process the company may follow in modelling earthquake risk

Answer 67

• The company will likely need to purchase model output from a company that is an expert in modelling earthquakes as this is different to the core business of employees of the insurer.
• The model output will include something along the lines of potential earthquake events with their associated locations, severities and frequencies.
• A simulation model would then be able to simulate whether each of the events happens or not in a particular year.
• The key modelling function is to then determine the cost to the insurer if each earthquake were to occur.
• This will be a function of the amount of exposure the insurer has (measured in terms of EML) at or within a near range of the location of the simulated earthquakes.
• For large buildings, the insurer may wish to model damage separately.
• The reinsurance model should be able to calculate recoveries on treaties.
• Key parameters should be sensitivity tested to understand model sensitivity to each factor and decide which factors are worth putting more time into estimating accurately, including more research.

Question 68

How might the calculation of economic capital differ from the calculation of regulatory capital?

Answer 68

Economic capital is typically calculated using an insurer’s own internal model, whilst regulatory capital would usually be calculated using a prescribed model or formula.

Economic capital would use a DETAILED BREAKDOWN of assets and risk exposures, using an insurer’s own risk profile, whereas regulatory capital would use data which are summariesd to a degree, and applying market risk profiles/characteristics.

The economic capital requirement may be on a more REALISTIC BASIS, without any prudence which may exist on a regulatory basis. Even a regulatory basis which is on a best estimate basis may include a risk margin which represents an adjustment for uncertainty.

Economic capital may use a HIGHER LEVEL OF CONFIDENCE than the regulatory figure, especially if this is a published risk disclosure.

Risks and events may be correlated in a very complex manner in an economic setting, whilst this is normally more simply applied in a regulatory setting.

Question 69

3 Main categories of ways in which reinsurance can improve an insurer’s solvency position.

Answer 69

An insurer’s solvency position is improved if its solvency margin increases relative to its solvency requirement.

Reinsurance can assist by:

• Increasing the value of the assets
• Decreasing the value of the liabilities
• Decreasing the regulatory minimum solvency requirement

Question 70

How could reinsurance help to increase the value of the assets? (4)

Answer 70

• Financing can be obtained through the reinsurance commission associated with proportional reinsurance.
• Financial reinsurance can be sought:
• – such arrangements can effectively be loans repaid from the future profits of the underlying business.
• – As the “repayments” of the “loan” are contingent on profits, they do not appear as a liability on the balance sheet, which would have been the case with a bank loan.

Question 71

How could reinsurance help in decreasing the value of the liabilities

Answer 71

• By reinsuring, the insurer is reducing the value of its liabilities as some are ceded to the reinsurer.
• Reinsurance allows the insurer to get a better spread of risks which may result in more certainty in aggregate results and therefore less need for margins in reserves.
• reciprocal arrangements can also assist with this.
• Non-proportional cover can assist in dealing with:
• – large claims
• – accumulations of risk

Question 72

How does reinsurance help to decrease the regulatory minimum solvency requirement?

Answer 72

• The required solvency level is often calculated with reference to the proportion of business reinsured, i.e., more reinsurance means a lower solvency requirement and therefore a stronger solvency position.
• However, this reduction may be subject to a limit, since there is a legal requirement for an insurance company’s free reserves to exceed a Required Minimum Margin.