Chapter 23 Reserves & solvency capital requirements Flashcards
1
Q
Reasons for calculating reserves
A
- to determine liabilities for published accounts
- to determine liabilities for solvency accounts
- to determine liabilities for internal management accounts
- to assist premium rating
- to value the insurer for merge and acquisition
- to influence investment strategy
- to assist with assessment of reinsurance arrangements
2
Q
Types of reserves: Long-term
A
- reserves for in-force policies = typically discounted value of future expected claims, expenses and premium cashflows.
- claims reserves (including IBNR) - disability claims
- claims reported but not fully settled.
- option reserves - additional costs that need to be set aside for the eventuality a particular option comses into the money.
- for group contracts, UPR and URR
3
Q
Types of reserves:Short-term
A
- UPR
- URR
- IBNR
- claims in transit reserves - reserves in respect of claim reported but not assessed or not recorded.
- OCR
- INBER
- equalisation or catastrophe reserve
4
Q
The role of statistical and case estimates:Long-term
A
- claim amount payable is known once claim is submitted, for most forms of long term insurance.
- however for annuity type contract period for which payments will carry on is not known.
- This may not be true for CI insurance, insurer will hold a reserve for claims reported but not fully settled, using amounts in policy docs and increase this by inflation where appropriate.
- reserves for benefits which provide income will be calculated using statistical methods.
- only small volume will be reserved for using case estimates. estimated using likely duration of claim.
- most of long term insurance provisions held are in respect of futre claims, acknowledging that a level premium pays cover of increasing probability of claim.
- actuaries may use deterministic or stochastic models to estimate potential claims outgo & set provisions.
5
Q
The role of statistical and case estimates:Short-term
A
-PMI is indemnity thus the amount payable is determined by costs incurred and is not known with certainty until treatment is complete.
- statistical approach is used to estimate amount of claim.
- although certain large claims will warrant case-by-case reserving.
- This involves calculating expected total claim amounts for outstanding claims based on relevant past experience.
- each claim is unique in that many different claim causes can arise, so cost of treatment can vary considerably.
6
Q
What should a claims manager take into account when estimating ultimate outgo for each case separately?
A
- procedure type
- hospital
- surgeon
- policy coverage (full indemnity, excess, limits, recuperation benefit etc)
- age,gender and past claims history
- current levels of medical inflation
7
Q
Statistical estimates
A
- this is appropriate for particular types of homogeneous claims where portfolio is large enough & is deemed to be stable.
- these methods estimate outstanding claims for cohorts based on historical trends and patterns, and adjusting for known or anticipated future changes.
- most statistical methods work from tabulations of claims that have recently been paid.
- portfolio might be segmented by contract type, distribution channel, location, etc.
- assumptions are made about the stability of claim development and past patterns will continue into the future.
8
Q
Basic chain ladder assumptions
A
- BCL assumes amount of claims paid in each development year from each origin year is a constant proportion of the total claim amount from that origin year.
- BCL assumes past inflation continues into the future.
- Inflation-adjusted BCL can be used
- Can also use inflation-adjusted average claim cost approach (Q4.17)
9
Q
The Borhhuetter Ferguson method merits
A
- Relies on assumed run-off patten and an estimate of the ultimate claims for each cohort.
- The estimate is usually made using the loss ratio method.
- The external estimate is apportioned between the past and future (as at the date of the reserving exercise).
- it improves on the crudeness of a loss ratio by taking into account information provided by latest development.
10
Q
Assumptions underlying the Bornhuetter Ferguson method
A
- underlying method is same as BCL.
- together with that the estimated loss ratio is appropriate
- this method could be viewed as using a Bayesian approach.
11
Q
Steps in calculating a reserve using BF method.
A
- Determine initial estimate of the total ultimate claims from each treatment month using premiums and initial expected loss ratios.
- Multipy these estimates by the proportion outstanding (1-1/f) determined from claims development table. These are estimates of the reserve for each treatment month.
- add these figures to the claims paid to date give an esitmate of the ultimate loss for treatment month.
12
Q
Explain boostrapping and what it is used for?
A
- It can be used to estimate the variance of the IBNR reserve.
- Shows the extent to which a reserve can vary on either side of its mean.
- A reserve method is chosen and used to produce a fitted model for historical data.
- The residual values are re-sampled with replacement to generate a number of pseudo run-off triangles.
- These pseudo run-off triangles can then be used to estimate the distribution of IBNR values.
13
Q
Weakness of statistical methods
A
- Outstanding claims might be impaired by the errors, omissions or distortions in the data, which invalidate the underlying assumptions.
- These distortions however do not mean the statistical methods should not be used.
14
Q
Assumptions underlying bootstrapping the BCL
A
- the run-off pattern is the same for each origin period
- incremental claim amounts are statistically independent
- the variance of the incremental claim amounts is proportional to the mean
- incremental claims are positive for all development periods.
15
Q
Distortions in data and results can occur due to a number of reasons
A
- external influences, such as inflation or changes in underlying nature of risk
- internal influences such as underwriting, claims settlement or recording procedures or reinsurance arrangements
- changes in the type of business attracted in each treatment class
- random fluctuation or large claims in a small portfolio.
16
Q
Principles of setting statutory or solvency reserves
A
- reserves should cover all liabilities arising from all contracts
- reserves should take credit for future premiums if these are contractually due to be paid
- reserves should be calculated prudently, allowing for all relevant liabilities
- valuation should be prudent, not best estimate, and so basis should contain margins
- valuation of liabilities should be consistent with the asset valuation
- approximations of generalisations may be allowed
- the interest rate used for calculating the reserves should be prudently taking into account the currencies, yields and reinvestment yields on the assets.
- demographic, persistency and expense assumptions used should be prudent but the expenses can be on an ongoing business basis.
- if valuation method itself defines the amount of expenses assumed then the amount implied must be no less than a prudent estimate of the relevant expenses.
- the valuation calculations conducted over time should not suffer discontinuities arising from arbitrary changes to the basis
- valuation method should recognise the emergence of profit appropriately over the policies’ lifetime
- valuation bases and methods should be disclosed.
17
Q
Discuss the need for solvency capital
A
- insurance supervisors reqiure that an insurer maintain at least a specified level of solvency capital in addition to reserves or technical provisions held.
- This solvency capital can be seen as providing an additional level of protection to policyholders.
- The level of SCR under regulation may be specified as a formula or it may be based on a risk measure such as VaR.
18
Q
Interplay between reserves and SCR
A
- when considering the adequacy of reserves to be set up it is important to do this within the context of SCR and not in isolation.
- Similarly the adequacy of SCR cannot be looked at in isolation of the reserving requirements.
- in some countries reserves are set up on a relatively realistic basis ie relatively small margins from the expected values.
- there us a requirement for a substantial level of SCR determined using risk-based capital tecniques.
19
Q
Value at Risk approach
A
- An example of a risk-based SCR approach is the use of a VaR measure.
- normally expressed at a minimum required confidence level (eg 99.5%) over defined period (eg one year).
- The supervisory balance sheet is subject to stress tests on each of the identified risk factors.
- A VaR of R10m with 99.5% means that there is only a probability of 0.5% of a loss greater than R10m.
20
Q
Other possible methods
A
- The run-off method
- Which looks at the amount of capital needed at the outset to ensure a firm’s ability to cover its liabilities until the last policy has gone off the books, allowing for suitable stresses to the risk factors.
- New business is ignored.
- applying stress tests to each different risk factor gives a capital requirement for each separate risk in isolation.
- In order to arrived at an aggregated capital requirement reflecting all risks these need to be diversified.
- This may be done using correlation matrices or copulas.
- Stochastic models are used to quantify the capital requirements in relation to economic risks.
- distribution used should properly reproduce the more extreme behaviour of the variable being modelled.
- these models are parameterised using historic parameters.
- distribution should not understate frequency of extreme case scenarios.
21
Q
Combining separate risks will lead to higher SCR than if if risks were combined using diversification matrices. What causes this?
A
- non-linearity
- non-separability of individual risks
22
Q
What is linearity?
A
-the capital required is a linear functions of the risk drivers.
23
Q
What is non-separability?
A
-refers to situations when if two events happen together, the combined impact is worse than if they happened separately.
24
Q
Market-consistent reserve methodology
A
- sometimes referred to as fair-valuation.
- this is the price someone would charge for taking responsibility for the liability, in a market in which such liabilities are freely traded.
- to determine the liabilities, future unknown parameter values and cashflows are set so as to be consistent with market values, where a corresponding market exists.
- in particular, assumed future investment returns are based on risk-free rate of return, irrespective of the type of asset actually held, and the discount rate rates are also based on risk-free rates.
- risk-free rates may be determined based on government bond yields or on swap rates.
- it would generally only appropriate to use swap rates if there is a sufficiently deep and liquid swap market in the country
25
Q
Market-consistent: Illiquidity premium approach
A
- corporate bonds typically have a higher yield than risk-free bonds. The
- the latter contributes to illiquidity premium.
- even under a market consistent approach it may be possible to take credit of illiquidity premium and thereby discount liabilities at a higher yield than risk-free rate.
- this would normally be restricted to long-term predictable liabilities for which matching assets can be held to maturity. Since insurer is not exposed to risk of changing spreads on such assets.
- where withdrawals & surrender values are permitted there would be strict rules about how and when illiquidity premium can be applied.
26
Q
Market-consistent: Risk margin
A
- it may be difficult to obtain a market-consistent assumption for some elements of the basis, such as morbidity, persistency or expenses, for which there is not a sufficiently deep and liquid market in which to hedge such risks.
- reinsurance quotes could give morbidity assumptions.
- expense agreements in the market could be used.
- it is then likely that a risk margin would reflect the compensation required by the market in return for taking on those uncertain aspects of the liability cashflows.
- this could be done by adding a margin to each such assumption or by using costs of capital approach.
27
Q
Describe the cost-of-capital approach to calculating the risk margins
A
- project forward the future capital that the company is required to hold in respect of its risks, at the end of each period.
- during run-off the business
- the required capital is determined according to relevant regulatory basis.
- these projected capital amounts are then multiplied by the cost of capital rate.
- this rate can be seen as the cost of raising additional capital in excess of risk-free rate.
- the product of cost of capital rate and the capital requirement at each future period is then discounted, using market-consistent discount rates.
- in some regimes it may be calculated as a fixed percentage of reserves.
- others can be complicated if the calculation of required capital itself requires projections.
- reserve run-off may be used as a proxy to how the capital will run-off.
28
Q
What is a passive valuation approach?
A
- relatively insensitive to changes in market conditions and has a valuation basis that is updated relatively infrequently.
~~~ -
(MM 4rm CA1 memory - methodology:Net prem typically, assumptions: less frequently updated)
~~~
29
Q
What is an active valuation approach?
A
- it is based more closely on market conditions with assumptions being updated on a frequent basis.
- (MM 4rm CA1 memory: typically gross premium methodology plus regularly updated assumps)
30
Q
Advantages of using a passive valuation approach?
A
- Passive valuation approaches tend to be more straightforward to implement, involve less subjectivity and result in relatively stable profit emergence.
- eg use of market-consistent valuation approaches for both assets, liabilities and risk-based capital approach to SCR.
31
Q
Disadvantages of using passive valuation approach
A
- out of date.
- insensitive to changes in market conditions.
- eg if stock market crashes then the book value of assets will be overvalued relative to their value if sold.
- similarly net premium valuation is relatively insensitive to changes in interest rates.
- important trends will not be taken account of due to infrequent updates
- may provide false sense of security.
32
Q
Advantages & disadvantages of active valuation approach
A
+more informative in terms of understanding impact of market conditions on ability of company to meet its obligations.
-results more volatile
-higher capital requirements may be required under equity market conditions using risk-based capital
-in order to reduce this companies would need to sell these assets which in itself could exacerbate the market conditions.
-more complex
