Chapter 21: Capital modelling - assessment of capital for various risk types Flashcards
Types of Capital
- Available/Risk Capital/own funds - excess of insurer’s assets over its liabilities - depends on the valuation basis, it could be on the basis of statutory balance sheet or insurer’s view i.e. economic balance sheet, it can be other. This is the same as free reserves, own funds, free assets.2. Economic/Required Capital - insurer’s own view of how much it should hold to fulfil management’s objectives (objectives are regulatory, then credit rating, market perception, more security for policy holders, confidence of investment analysts, other stakeholder requirements such as debt holders, business development objectives, etc., according to its risk appetite. Calculated from risk based captial model output eg. output of an internal model.3. Excess Capital - diff between total capital and economic capital4. Regulatory Capital/Solvency Capital - Amt required by regulator. Because regulators want to protect PH interests and they want to have the confidence that insurers can pay claims. Eg. Solvency - SCR, MCR Some regulators need a prudent valuation basis whereas other regulators may want a best estimate basis.”
Available capital
The excess of an insurer’s financial assets over the value of their liabilities.
Required capital
The amount of capital an insurer needs to set aside to allow the insurer to withstand losses.
2 Main types of required capital
- regulatory capital
- economic capital
Regulatory capital
(a.k.a. solvency capital)
An amount of capital an insurer is required to hold for regulatory purposes.
Economic capital
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.
“Economic Capital - how it is determined(Internal Model meaning/basis)”
“It is determined by an internal model which means a capital model developed internally specifically to measure the insurer’s risks.It is based on
A RISK BASED CAPITAL ASSESSMENT
a) the risk profile of the assets and liabilities of the insurer
b) the correlation between those risks
c) tolerance level desired for credit deterioration in adverse cases”
Economic Balance sheet is made up of
“On the basis of a risk based capital assessment, it has Market value of Assets (MVA) less Market Value of Liabilities (MVL) = Insurer’s available capital
Why might an insurer hold more capital than the minimum specified by regulators? (6)
- 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).
Economic capital will typically be determined based upon (3)
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.
internal model
a capital model developed internally specifically to measure the insurer’s risks.
It is commonly used to determine the amount of economic capital required.
Economic balance sheet (3)
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
A risk profile is fundamentally defined by (2)
- the risks that have been modelled (and the way in which they have been modelled)
- the key outcome used to measure success or failure
The key outcome here is a financial outcome such as a surplus balance sheet position at the end of a selected time horizon.
Risk measure
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. An example is VaR
Risk tolerance
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
for example, a risk tolerance of 0.5% would set capital such that there is one in 200 chance that the b/s position at the EOY shows a deficit.
(i) Suggest how the firm’s business activities might be hampered if its available capital fell below the regulatory requirement.
(ii)
Explain why it is important that ratings agencies and investment analysts believe that insurers are holding sufficient solvency capital
(i)
Falling below the regulatory minimum
1. 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.
2. 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:
a. limiting the levels of new business sold
b. closing to new business
c. changing the investment strategy to a more matched position
d. or to invest in less volatile asset classes
e. appointing a custodian of its assets
f. increasing the amount of reinsurance the insurer has in place.
(ii)
Perception of solvency
1. The views of rating agencies and investment analysts will affect:
2. the credit rating of the insurer
3. the credit rating of the debt issuer
4. the attractiveness of lending to the insurer
5. the attractiveness of buying shares in the insurer
6. the appeal of the insurer’s products
7. the insurer’s standing in the market
Explain why an insurer will not wish to hold too large an amount of capital in excess of its economic capital requirement.
Capital has a cost, ie the providers of the capital will require a return on their capital. All else being equal, holding a larger amount of capital means that a given level of profit is spread more widely amongst the providers of capital.
6 Common risk categories in a capital model
- insurance risk
- market risk
- credit risk
- operational risk
- group risk
- liquidity risk
Insurance risk
The risk of loss arising from the inherent uncertainties about the occurrence, amount and timing of insurance liabilities, expenses and premiums.
Reserving risk
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
2 Components of insurance risks and how is it mitigated? and what are the other overall considerations in insurance risk?
- underwriting risk, (relating to risks yet to be written / earned)
- reserving risk (relating to risks already earned)
Insurance risk is mitigated by ceded reinsurance, so the capital requirement depends on the net liabilities.
Overall - Other considerations
Other considerations affecting the assessment of the capital impact of insurance risk are:
a. Underwriting cycle: the base model should reflect any expected movement of rates, terms and conditions, premium volumes, and claims, with rising loss ratios in a softening market. Where the trend is uncertain, the model should reflect this through increased variability.
b. Parameter error: we should include a margin in the variability assumptions to allow for less than full credibility of historical data. This is especially the case for any new classes, or any rapid expansion of a class that might take it beyond the firm’s niche sources of business or areas of underwriting expertise.
A rapidly expanding class may also be subject to different (ie more attractive) terms and conditions, and may be attracting a different mix of policyholders than previously. Therefore a credible set of relevant data may not yet be available.
c. Reinsurance of unexpired risk: if reinsurance is purchased on a losses-occurring basis, then the insurer will not yet have purchased reinsurance to cover the (future) period that is being modelled. Therefore the capital model should either:
assume that this reinsurance will not be bought, or allow for the likely cost of purchasing this reinsurance.
d. Multi-year policies: if a firm writes policies with multi-year risks or guaranteed future premium rates, or if it makes other underwriting commitments whose risk runs beyond the end of its modelling period, such as binders, we must model these so that the firm’s insurance risk capital will suffice for all risks taken on during the period.
e. Management actions: in a multi-year model, we may assume that following underwriting losses the firm will increase rates, providing we can demonstrate that it has responded to past losses in this way. However, we should allow in the model for the lags before the losses become apparent, in deciding to increase rates and in imposing those increases. We should be wary of assuming an increase following a loss not shared by the market, since if the competitors are not also raising rates, competitive pressures may prevent the firm from doing so.
f. Discounting: unless the regulator has specified otherwise, it may be acceptable to model using either discounted or undiscounted reserves. If using discounted reserves, discounting should only impact insurance risk to the extent that the impact relates to any change in future payment patterns. (Any impact from change in discount rate should belong to market risk.)
Consider the capital impact of gross underwriting risk.
or considerations you should take into account when modelling gross u/w risk
- Data required to measure underwriting risk
(i) As a starting point, we can consider the firm’s business plan if this is prepared on a realistic basis. If the firm uses an aspirational business plan for motivational purposes, this should first be adjusted to a best estimate basis.
(ii) We should be able to support the loss and expense ratios for each class by reference to historical performance, after adjusting for changes in rates, terms and conditions.
(iii) For a new class, or one with insufficient internal experience, we should be able to support the assumptions by reference to market experience, after adjusting for any differences.
(iv) The capital requirement for the underwriting risk is the difference between: :
the underwriting result at the firm’s chosen level of risk tolerance for the business written / earned during the modelled period, and
the underwriting result on the realistic basis.
(v) One way to apply a realistic basis would be to exclude any profit expected (deducting any such baseline profit from the capital requirement as a separate item). It would then be based on projected eventual results, that is, with best estimates of the ultimate cost of claims.
Additional points:
(i) The insurer will need to project its underwriting result over the appropriate time horizon.
(ii) The risk is that actual experience is different from that expected.
(iii) an insurance company will need to estimate the volumes and mix of business that it will write (or the earnings profile of business that it has already written).
(iv) The projection should be on a best estimate basis - Measuring underwriting risk
To determine the capital requirement for the underwriting risk at the chosen level of risk tolerance, we should divide the firm’s business into classes / currencies / territories of sufficient granularity (that is, small enough subdivisions) that we can consider distinctive features of the class, but not so fine that statistical methods become invalid (because of insufficient data in the subdivisions).
We should then assess the variability of its claims and expenses, either by fitting statistical distributions or by simpler approaches such as stress tests.
Claims should generally be split into the following classes:
-attritional claims
-large claims
-catastrophe claims
-future latent claims. - Modelling attritional claims
- We 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.
- For classes that are small or not subject to large claims it may be more practical to model loss ratios rather than separately model individual large claims. - Modelling large claims
- Ideally, we should model large claims separately from attritional claims so that we can determine reinsurance recoveries directly. (The dividing line between large and attritional claims is often the firm’s typical retention for policies in the class.)
- We generally model large claims on a frequency-severity basis
FREQUENCY:
-The Poisson and negative binomial distributions are often used for frequency. The Poisson distribution is only appropriate where the occurrence of claim events are independent, since if there is any correlation between claim events, this distribution will underestimate the tail risk.
-If claims are independent and occur completely randomly, they may conform to a Poisson process, in which case claim numbers would have a Poisson distribution. However, if there is any correlation between claims, then a Poisson distribution may not be appropriate, as it will underestimate the number of claims.
SEVERITY:
-For severity, sampling from revalued past claim sizes is sometimes used, but this omits the risk of a claim greater than experienced in the past, so it is preferable to fit a distribution.
-A heavily-skewed distribution such as the Pareto would normally be appropriate for severity, and we should derive it from or test it against historical data revalued to current claims costs.
ENIDs:
For both attritional and large claims, it will be necessary to consider if there are any types of claims that are not present in the historical claims data used for parameterising the distributions. These are often referred to as Events Not In Data (ENIDs). It may be appropriate to increase the standard deviation of the distributions beyond that derived purely from historical data to allow for ENIDs.
If we believe that there is a risk of large losses arising that is greater than those experienced in the past, we should make an assumption about the likely severity and frequency of these, and ensure that our fitted frequency and severity distributions allow for these adequately.
This assumption may be subjective due to the lack of detail in the historical data. However, information may be available from underwriters, reinsurers, brokers, etc.
Similarly, if the historical data includes unusually heavy experience, then it should either be adjusted to reflect likely future experience, or the fitted distributions should reflect this
- Modelling catastrophe claims
- We should model catastrophe-type claims separately from either attritional and large claims, especially for events that may impact more than one class.
- We often cannot model catastrophe events from the firm’s experience because of their rarity.
- Due to their different nature, natural, man-made (here called human-made) and terrorist-based catastrophes may be modelled in different ways:
- For natural catastrophes such as earthquake or windstorm, or for terrorist attack, a proprietary model can apply a set of simulated events to the firm’s exposure to derive a distribution of possible costs.
- It is the firm’s responsibility to ensure that the model is suitable; for example, by allowing for demand surge, climate cycle, and so on, and to test the results against the known impact of recent actual catastrophes and to resolve or adjust for any discrepancy.
- For human-made catastrophes other than terrorism, the firm is likely to have to develop a bespoke model.
- For example, for the effect of a severe recession on its creditor business, we might assess the impacts of recessions of various depths, and then model the drivers or indicators of recession to fit a distribution to these costs - Modelling future latent claims
- Finally, we may need to consider future latent claims as a separate risk.
- As with catastrophe claims, insurers are unlikely to be able to model future latent claims based on past experience.
3 Risks included under underwriting risk
- claims higher than expected
- premium volumes lower than expected
- expenses higher than expected eg related to mix of business
4 Categories of claims that should be analysed separetly
Attritional claims
- large claims
- catastrophe claims
- future latent claims
How are future latent claims modelled?
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.
The capital impact of the reserving risk
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 claim
Suggest why past claim sizes might not reflect likely future experience.
past claim sizes might not reflect likely future experience because there may be changes in:
- risk due to a change in the mix of underlying risks
- the method of distribution (ie sales channel)
- cover / policy terms and conditions
- underwriting strategy, eg policy acceptance
- claims handling strategy
- claims inflation, which may depend on inflation of: –
- -prices
- -earnings
- -medical costs
- -court awards
- new procedures / types of claims
- the level of reinsurance coverage
- environment, including:
- -legislation / regulation
- -advances in technology
- -medical advances
- -processes for building / repairing property.
Suggest why we would model large claims separately from attritional claims.
Loss ratios will be distorted – possibly significantly – by the existence of large claims. However for classes that are small or not subject to large claims, the effect of this may be minimal.
Explain why insurers are unlikely to be able to model future latent claims based on past experience.
This is due to the heterogeneity of latent claim types, eg pollution claims exhibit very different characteristics to asbestos claims, and future latent claims will probably exhibit very different characteristics from these
Consider capital impact of gross reserving risk.
Modelling reserving risk.
- Data required to measure reserving risk
(i) As a starting point, we can consider the firm’s actual reserves if these are prepared on a best estimate basis.
(ii) If the firm includes a significant reserve margin in its published reserves, we should first remove this.
(iii) We should be able to support any assumptions made in the reserving, such as any initial loss ratios used for Bornhuetter-Ferguson projections, by reference to earlier years’ results or, if necessary, benchmarks, after adjusting for changes in rates, terms and conditions.
(iv) Other adjustments will also need to be made, as we outlined above.
(v) The capital impact of the 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 on a best estimate basis
(vi) Thus, it should not include any reserve margin. (Any reserve margin, if sufficiently evidenced, may be added to the capital resources available to meet the capital requirement.) - Measuring reserving risk
(i)To determine the capital impact of the reserving risk at the chosen level of risk tolerance, we should divide the firm’s business into classes of sufficient granularity, but not so fine that statistical methods become invalid.
This is analogous to the method used to measure underwriting risk.
(ii) This may be at the granularity used for reserving, but we need more data to assess variability than to assess a best estimate, so it may be necessary to group classes of similar reserve variability.
(iii) We should then assess the variability in the firm’s claims settling, by statistical techniques such as bootstrapping or the Mack method, or by simpler approaches such as stress tests. - Additional risks
(i) We should consider whether sufficient historical reserve shocks have occurred to indicate possible future variability (ie whether ENIDs are allowed for).
(ii) Where this is not the case, we could either adopt a greater variability than the historical figure, or we could model an explicit shock such as a future Ogden rate change.
(iii) It is unlikely that future latent claims will be adequately represented, since these are generally removed from claims data and reserved separately.
(iv) Therefore, we should consider latent claims separately, perhaps by a stress test in view of the difficulty in modelling their risk with any precision.
(v) A firm may choose to model material claims separately, eg a large immature catastrophe event.
Reasons for this may include:
-the presence of the claim distorting the variability analysis for the affected lines of business
-the reserving team may have already carried out specific analysis over the volatility of the loss
-extreme uncertainty over the ultimate cost
-specific reinsurance arrangements
-better management visibility of the impact of the claim.
(vi) If no latent claims have yet emerged on business already written / earned, then we would expect the methodologies used in estimating the underwriting risk and reserve risk for latent claims to be consistent.
