Chapter 22: Capital modelling Flashcards
(93 cards)
1
Q
The aim of a capital model
A
Used to help the insurance company determine the level of capital to hold.
The model should also enable the company to better understand their risks and will inform business decisions
2
Q
Available capital
A
The excess of an insurer’s financial assets over the value of its liabilities.
3
Q
Required capital
A
The amount of capital an insurer needs to set aside to allow the insurer to withstand losses.
4
Q
Main types of required capital
A
- Regulatory capital
- Economic capital
5
Q
Regulatory capital
A
AKA Solvency capital
The amount of capital an insurer is required to hold for regulatory purposes
6
Q
Economic capital
A
The amount of capital the provider determines is appropriate to hold given its assets, liabilities and business objectives.
This will be greater than the minimum regulatory capital.
7
Q
Reasons why insurers hold more capital than the minimum specified by their regulators
A
- to reduce the risk that the available capital falls below the regulatory requirement, which would hamper the business’s activities
- to give a greater degree of security to policyholders than implied by the relatively weak regulatory minimum
- to maintain its credit rating
- to meet requirements of other stakeholders, such as debt providers, whose interests may be subordinated to those of policyholders
- to maintain a level of working capital for investments in business development and other opportunities
- to allow a buffer between actual profitability of the business and the dividend stream paid to shareholders, who prefer less volatile returns
8
Q
How might the firm’s business activities be hampered if its available capital fell below the regulatory requirement?
A
If the level of available capital falls below the regulatory requirement, then the regulator will intervene to protect the interests of existing or prospective policyholders.
Depending on the severity of the situation, the regulator may require the insurer to establish a recovery plan, which will be monitored closely by the regulator. Such a plan might include:
- limiting the levels of new business sold
- closing to new business
- changing the investment strategy to a more matched position or to invest in less volatile asset classes
- appointing a custodian of its assets
- increasing the amount of reinsurance the insurer has in place.
9
Q
Why is it important that rating agencies and investment analysts believe that insurers are holding sufficient solvency capital?
A
The views of rating agencies and investment analysts will affect:
- the credit rating of the insurer
- the credit rating of the debt the insurer issues
- the attractiveness of lending to the insurer
- the attractiveness of buying shares in the insurer
- the appeal of the insurer’s products
- the insurer’s standing in the market.
10
Q
Economic capital will be determined based upon:
A
A 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
11
Q
Internal model
A
A capital model developed internally specifically to measure the insurer’s risks
It is commonly used to determine the amount of economic capital required.
12
Q
Economic balance sheet
A
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)
13
Q
Capital models can be characterised by core features:
A
- risk profile
- risk measure
- risk tolerance
14
Q
Core features of capital models:
Risk profile
A
The risk profile is defined fundamentally by:
- the risks that have been modelled (including the way in which they have been modelled)
- the key outcome used to measure success or failure
Risks modelled are typically those arising from business that has already been written and a finite period of new business activity.
A financial outcome is typically used as a measure of success or failure.
15
Q
Core features of capital models:
Risk measure
A
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 a time horizon.
16
Q
Core features of capital models:
Risk tolerance
A
The risk tolerance is 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
17
Q
Common risk categories used to group uncertainty related to cashflows
A
- insurance risk
- market risk
- credit risk
- operational risk
- group risk
- liquidity risk
18
Q
Insurance risk
A
The risk of loss arising from the inherent uncertainties about the occurrence, amount and timing of insurance liabilities, expenses and premiums
19
Q
Components of insurance risk
A
- underwriting risk
- reserving risk
20
Q
Risks included under underwriting risk
A
Risk that:
- claims higher than expected
- premium volumes lower than expected
- expenses higher than expected e.g. related to mix of business
- etc.
21
Q
Underwriting risk
A
Insurance risk relating to risks yet to be written/earned
22
Q
Reserving risk
A
Insurance risk relating to risks already earned.
Will cover the risk that claims and/or expenses on expired business turn out higher than the reserves held. This may be from:
- underestimating development on notified claims (IBNER)
- underestimating IBNR
23
Q
Certain factors affecting the underwriting result are specifically included in other risk categories and hence should not be included in insurance risk. These include:
A
- Any risk to gross liabilities through non-collection of reinsurance falls under credit risk
- Any risk to the payment of gross liabilities through poor investment performance falls under market or liquidity risk.
- Any risk to the writing of premiums or the settling of claims arising from control failure, rather than from market uncertainties, falls under operational risk
- The risk of reserves being insufficient to meet liabilities due to lower investment return than expected (assuming discounting is used when calculating reserves). This falls under market risk.
- Consequent changes in the value of the insurance liabilities due to changing interest rates also falls under market risk. (this is relevant if liabilities are valued on a mark-to-market basis).
24
Q
Market risk
A
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
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Market risk can be divided into:
- consequences of changes in asset values
- consequences of changes in the value of liabilities if these are values on a mark-to-market basis
- consequences of a provider not matching asset and liability cashflows
26
Sources of general market risk
Movements in:
- interest rates
- exchange rates
- equity prices
- real estate (property) prices
27
Credit risk
The risk of financial loss due to another party failing to meet its obligations, or failing to do so in a timely fashion.
28
Categories of credit risk
- 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.
29
Operational risk
The risk of loss due to inadequate or failed processes, people or systems or from external events
30
Group risk
The risk a firm experiences from being part of a group as opposed to being a standalone entity
31
Liquidity risk
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
32
Stochastic model
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 a range of different outcomes.
33
Stages in building a stochastoc model
- 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 variables to be modelled stochastically
- estimate the parameters that should be used for each variable
- test and validate the reasonableness of the assumptions and their interactions
- ascribe values to the variables that are not being modelled stochastically
- construct a model based on the chosen density function(s)
34
Running a stochastic model
- 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
35
Advantages of a stochastic model
- Stochastic models test a wider range of scenarios
- We can derive a probability distribution from the outcomes of a stochastic model and calculate confidence levels, if required
- The model is at least explicit about the assumptions being made. We can also test the assumptions by different techniques
- We can derive a probability distribution from the outcomes of a stochastic model and calculate confidence levels, if required. This is not the case with a stochastic model
36
Advantages of a deterministic model
- model is usually easier to design and quicker to run.
- reducing the computational power necessary to generate many thousands of simulations, we can introduce more detail in other dimensions
- important that users of the output understand the results from the model – we can often make the results more comprehensible to them.
- easier to communicate the results of stress and scenario tests to senior management
- more readily explicable to a non-technical audience
- help to link the capital model with the risk register, helping to integrate capital and risk management
- it is clearer what economic scenarios have been tested - there is a danger that certain scenarios, which could be particularly detrimental to the company, are not identified.
37
How are attritional claims modelled?
- Generally model attritional claims in aggregate.
- A mildly-skewed distribution such as the lognormal may be appropriate, although we should test this against experience.
- If the standard deviation is a sufficiently small fraction of the mean, a normal distribution may be an adequate approximation.
- can be modelled as a percentage of exposure (or premium) to allow for the effect of increased risk exposure on claims. This can be thought of as the part of the loss ratio attributable to attritional claims.
38
When analysing claims, they should be split into the following classes:
- attritional claims
- large claims
- catastrophe claims
- future latent claims
39
How are large claims modelled?
should model large claims separately from attritional claims as they have the potential to distort the loss ratio significantly
Generally model large claims on a frequency-severity basis:
- Poisson distribution is often used for frequency, but is only appropriate where the claims are independent
- sampling from revalued past claim sizes is sometimes used, but this omits the risk of a claim greater than experienced in the past for severity.
- heavily-skewed distribution such as the Pareto often used for severity
40
How are catastrophe claims modelled?
Ccannot model catastrophe events from the firm’s experience because of their rarity.
Due to their different nature, natural, man-made and terrorist-based catastrophes may be modelled in different ways.
Proprietary models may be used
41
How are future latent claims modelled?
As with catastrophe claims, insurers are unlikely to be able to model future latent claims based on past experience.
A more approximate approach such as a subjective loading is likely to be used.
42
The capital impact of the reserving risk (Gross reserving risk)
Is 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, and
- the current reserves held for those claims
43
What might the current reserves not allow for?
- possible future volatility owing to reserve shocks
- future latent claims
44
Methods of allowing for reinsurance
- assume that the gross to net ratio will remain the same as previous years
- calculate reinsurance recoveries directly
45
Methods of allowing for reinsurance:
Gross to net ratio will remain the same as previous years problems
This method does not take into account specific details of the claims experience and reinsurance treaties, including:
- recoveries on individual losses
- aggregate limits (incl. aggregate limits on proportional treaties)
- reinstatements (and exhaustion of cover)
- catastrophe claims
46
When allowing for reinsurance when calculating capital requirements, what do we not need to allow for?
We do not need to allow for:
- reinsurance failure (credit risk)
- lack of cover through mis-purchase (operational risk)
47
Other considerations affecting the assessment of capital impact of insurance risks
- underwriting cycle
- parameter error - allow for less than full credibility of historuc data
- multi-year policies - extend its risk modeling to reflect the true duration of the risk exposure
- management actions - allow for lags before losses become apparent and premiums are adjusted
- reinsurance terms
48
Factors to consider when modelling market risk
- 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 on the liabilities should also be considered, so that market risk on the net solvency position can be assessed
49
Approaches to model market risks and assets chosen
- model each asset individually
- group similar assets
- model a notional portfolio
50
Methods of modelling market risk
- simple stress testing
- using an economic scenario generator (ESG)
51
Examples of stress test approaches when modelling market risk
- a rise in interest rates of W% leading to reduced asset values
- an X% fall in equity prices
- currencies depreciating against the rand by Y%
- a fall in property values by Z%
- a change in the spread of corporate bonds/yields
52
Considerations when using a stochastic modelling approach to assessing investment credit risk
- the probability of default by each counterparty
- the degree of default, that is, the loss when default occurs
53
General considerations when modelling investment credit risk
- spread risk - risk that credit spread doesn't remain constant in future
- correlations between counterparties and between asset classes
- correlations between assts may be due to underlying correlations with the financial and economic modelling factors used in the assessment of market risk. The modelling of market and credit risk should thus be consistent
54
Considerations in model of counterparty credit risk
- probability of default
- loss when default occurs
- increased risk of reinsurance failure in extreme loss scenarios
- correlate reinsurance failure rates with severity of losses in large loss scenarios
- correlation with individual insurer
- duration of liabilities - higher probability of default on more distant recovery
- correlation between counerparties
- non-recoveries due to reinsurance disputes and extent to which this isn't considered in operational risk
- collateral held by the insurer, which can be realised in the event of a default
55
Credit risk:
In designing suitable scenarios, it's important to consider:
- potential "ripple" effects
- hidden costs of adverse credit scenarios
56
Credit risk:
Examples of stress tests
- failure of largest reinsurer
- existing/possible future disputes relating to reinsurance contracts on a pessimistic basis that aren't reflected in the value attributed to the reinsurances
- failure f largest intermediary
- one notch downgrade of all reinsurers and impact on output of the stochastic model if rating inputs were changed
- default of the most significant corporate investment
57
Difficulties with operational risks
- to judge which risks we have already allowed for appropriately so we can avoid double counting
- identify which risks have been omitted
58
Modelling operational risks
- identify all material operational risk scenarios specific to the firm’s business
- requires considerable input from owners, senior management and other individuals who have a detailed working knowledge of the operations of the business
- difficult to assess and requires judgement and experience
- broad-brush measures are not generally accepted
- stochastic techniques in assessing the capital impact of operational risk, although this is infrequent
- make judgements about the degree of loss that each risk may give rise to, the type of event that may cause the loss and the frequency of such a loss occurring
- consider each loss gross and net of any mitigating controls
59
Group risk mitigation
- capital is not a good mitigant of group risk
- more effective mitigant is the introduction of effective management controls, and an enterprise risk management (ERM) policy
60
Modelling liquidity risk
When we model liquidity risk we are not calculating how much capital to hold to cover liquidity risk, but rather how much of the capital (held for other risks) to be held in liquid assets.
Modelling liquidity risk involves assessing the cashflow of the business (including timings) and comparing the required cash outflow at any point in time to the available liquid assets
61
Alternatively (or as a complement to the stochastic method), the following stress tests can be used to assess liquidity risks
- an increase in attritional claims
- a delay between a large loss and receipt of corresponding reinsurance recoveries
- a catastrophe loss occurring
- a reduced level of new business and the associated impact on the insurer's ability to pay claims on expired business
62
Alternative approaches of allowing for correlations
- consider cause and effects to assess the key drivers of correlation
- consider the likely scenarios in which the particular risks will occur at the same time
63
Implementing correlations in a capital model
- linking assumptions (leading to implicit correlations)
- explicit correlations between distributions
64
Aggregation when using a deterministic model
- Include known correlations in the deterministic scenarios generated. Here, linking assumptions can be used in the model to help inform the scenario output.
- Apply the standard methodology for summing variances of distributions. If we assume that we can combine capital amounts in the same way as standard deviations of distributions, then the above formula can be applied to capital amounts, rather than variances. However, where the capital amounts are extreme percentiles in the tail of skewed probability distributions, this may not be mathematically correct
65
Types of correlation to allow for:
- underwriting classes of business
- risk types
- successive years
- legal entities within a group
66
Allocating the total capital held between classes, products or individual policies may be necessary for:
- performance measurement
- business planning and strategy setting
- pricing
67
Reasons why capital allocation is necessary:
Performance measurement
Capital has a cost. To accurately assess the performance of, say a class, we need to calculate the profit/return as a percentage of the capital required to write that class, i.e. a return on equity
68
Reasons why capital allocation is necessary:
Business planning and stretegy setting
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.
This can be extended when deciding on which new ventures / products / territories to pursue.
69
Reasons why capital allocation is necessary:
Pricing
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.
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Methods of allocating capital
- percentile method
- marginal capital method
- Shapley method
- proportions method
71
Capital allocation:
Percentile method
The percentile 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.
When we allocate the capital, we may:
- use a different risk measure from that used in assessing the capital requirement
- allocate the diversified capital down to individual classes of business or products for a company in the group with reference to a lower percentile or with reference to various percentile-defined layers to prevent over-allocation to catastrophe-type business.
72
Capital allocation:
Marginal capital method
AKA "last in" method
- We allocate the capital with reference to the marginal capital requirements of each segment
- we allocate the capital with reference to the marginal capital requirements of each segment
- different level of capital allocated to different classes of business or product depending on the order in which capital is allocated to the different classes / products
73
Capital allocation:
Marginal capital method
Why are there different levels of capital allocated depending on the order of capital allocation?
This is because a class of business will be correlated with other classes to different extents. Therefore the additional diversification benefit to be gained by “adding” another class of business to the portfolio will depend on which classes have been “added” so far.
74
Capital allocation:
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 and so on.
The advantage of this method is that the allocated capital is not dependent on the order in which it is allocated to each class
The method can be unworkable in practice. The number of scenarios that needs to be run is the factorial of the number of classes.
75
Capital allocation:
Proportions method
We 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 each of these is of the total of the individual capital requirements. (Note that this does not yet allow for any diversification benefits in the aggregate amount, it merely gives us the proportions we need to allocate the capital between classes.)
We then calculate the aggregate capital requirement, allowing for any diversification benefits, and allocate this to each class, according to the proportions calculated above.
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Types of capital to allocate
- total capital
- economic capital
- excess capital
economic capital + excess capital = total capital
77
Reasons a company may hold more capital than its capital model may suggest is needed
- increase business volumes by providing a high degree of confidence that it can meet its obligations to policyholders
- benefit from cheaper financing terms to improve its standing in the market in the eyes of investment analysts
- reduce the risk of having to call on shareholders or members for further finance if losses are greater than expected
- smooth dividends to shareholders, who prefer less volatile returns
- meet the requirements of other stakeholders, eg debt providers, whose interests may be subordinated to those of policyholders
- enable it to develop the business, eg launching new products or for financing the takeover of a rival insurer
- enable it to undertake a more aggressive investment (and hence pricing) strategy
- manage unexpected cashflow mismatches, eg claim payments that cannot be met by investment and premium income
78
Uses of data in a capital model
- to create a model of the business as at the run date of the capital model
- as inputs to selecting assumptions used to simulate the firm's results and capital over the period covered by the capital model
79
Main items of data needed to create a model of the business
- 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
- costs of future reinsurance
- 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
- total reinsurers’ share of gross unpaid claims with, to the extent that it can be ascertained, each reinsurer’s share of the total
- reinsurance programme to which claims arising from unexpired business is subject or planned programme
- planned reinsurance programme to which claims covered by the model are subject
- expenses of the firm
- value of assets by asset category (other than the reinsurers’ share of technical provisions as this is covered above)
- credit exposures; for example, broker balances.
- details of operational risks – normally identified in a risk map
80
We should aim to use a business classification in the capital model that:
- others in the firm will be able to identify with and buy into
- is not at too high a level such that the accuracy of the results from the capital model would be unacceptable (that is, too few groups so that some groups are too heterogeneous)
- is not at too detailed a level such that the model becomes overly complex, has overly long run times, or parameter error for many of the classes becomes unacceptably high because there is paucity of data in many of the classes.
81
Assumptions needed to simulate quantities for the various components of the capital model
- 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 (including claim management costs) 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.
- proportion of reinsurers’ share of gross claims that the firm is unable to recover, by reinsurer.
- reinsurance exhaustion.
- reinsurer downgrade assumptions (possible change in default risk).
- expenses, acquisition and administrative.
- inflation and investment returns by asset class.
- operational losses
- tax and dividends
- relationships / correlations between different components of the model.
82
Features of a good model
- model chosen should reflect adequately 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
- outputs from the model and the degree of uncertainty surrounding them should be capable of independent verification for reasonableness and should be readily communicable
- 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
- model should be sufficiently flexible
- model should be capable of development and refinement
- range of methods of implementation should be available to facilitate testing, parameterisation and focus of results
83
Additional features of a good stochastic model
- have all parameters clearly identified and justified
- be structured and documented so that it can be understood by senior management 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 (for example, 10,000 or even 50,000)
- have a robust software platform.
84
General modelling considerations
- all parties involves should understand the whole process
- the model developers should understand the business deeply
- the objectives of the model relate to an increased understanding of risk and capital by management, and decisions including the impact on risk and capital
- there are a number of decisions that a capital model can inform
- 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
- the principle or proportionality and practicality should be considered when deciding on the level of detail to model
- 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
85
Key objectives of any capital modelling regime
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 (prior 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. Regulators may have a “use test” to assess this.
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How the capital model may be used to inform management decision making
- reinsurance
- investment
- pricing
- reserving
- strategy
- risk management
87
How the capital model may be used to inform management decision making in:
Reinsurance
Optimising the purchase of reinsurance – this may involve deciding on the retention level that optimises the savings in reinsurance premiums and the capital required
88
How the capital model may be used to inform management decision making in:
Investment
Assessing the impact of a change in the investment mix on the capital required and expected return
89
How the capital model may be used to inform management decision making in:
Pricing
Assessing return on capital for pricing and performance measurement
90
How the capital model may be used to inform management decision making in:
Reserving
Quantifying the uncertainty in claims reserves – the capital model may be used to give a range of outcomes around a deterministic best estimate. Although, this could be done separately to the capital model
91
How the capital model may be used to inform management decision making in:
Strategy
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.
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How the capital model may be used to inform management decision making in:
Risk management
Identifying key risks based on the model output and assessing the impact of mitigation
93
How might the calculation of economic capital differ from the calculation of regulatory capital?
Compared to a regulatory capital requirement, which often incorporates a degree of prudence, the risk-based requirement may well be measured on a more realistic basis, although the difference between economic and regulatory capital depends on the regulatory regime.
Depending on the insurer and its regulatory regime, either economic or regulatory requirements may drive the eventual capital held.
Differences between economic capital requirements, regulatory capital requirements and the output from a ratings agency’s model can normally be attributed to different approaches to approximations or differences in the nature or level of protection required.
