Chapter 23 - reserving Flashcards
1
Q
The purpose of calculating reserves
A
ARMIC
- determine liabilities to show in published accounts
- determine liabilities to be shown in supervisory accounts (if separate accounts have to be prepared)
- to determine liabilities to be shown in internal management accounts
- assist with assessment of reinsurance arrangements
- value the insurer for merger or acquisition
- influence investment strategy
- estimate the cost of claims incurred in recent periods and hence provide a base for estimating future premiums required to attain a given level of profitability
2
Q
Reserves for short-term
A
- UPR
- URR
- IBNR
- claims in transit
- outstanding claims reserve
- incurred but not enough reported
- equalisation or catastrophe reserve
- investment mismatch
3
Q
UPR
A
The balance of premiums received in respect of periods of insurance not yet expired
4
Q
URR
A
- reserve in respect of the above unexpired insurance premium where it is felt that the premium basis is inadequate to meet future claims and expenses.
- URR is an estimate of what is actually needed to provide for the unexpired risk
- calculated by estimating the future loss ratio and applying it to the proportion of premium unexpired
5
Q
Claims in transit
A
reserve in respect of claims reported but not assessed or recorded
6
Q
Outstanding claims reserve
A
reserve in respect of claims notified to the insurer but not fully settled
7
Q
IBNER
A
- reserve for outstanding reported claims
- adjustment to existing outstanding claims reserve
8
Q
Equalisation or catastrophe reserve
A
reserves where it is felt that the current year and abnormal amounts will have to be held back for abnormal events.
9
Q
Methods to calculate reserves
A
- case estimates
- statistical estimates
10
Q
when would you use statistical estimates for long-term?
A
Usually used where benefits are paid as an income
11
Q
When would you use case estimates for long-term?
A
Would only be used for very small volumes of claims, where the reserve can be determined by asking the claims manager to estimate the likely duration of each claim (where claims payments form a known income)
12
Q
When would you use statistical estimates for short-term?
A
PMI (although certain large or unusual claims will warrant reserves on a case-by-case basis)
- statistical estimation involves calculating the expected total claim amounts for outstanding claims based on relevant past experience.
13
Q
Claims estimates
A
claims manager inspects claims papers and estimates the ultimate outgo for each case individually
14
Q
What factors for PMI will be taken into account when calculating claims estimates?
A
- procedure type
- hospital to be used
- name of surgeon, consultant, or other medical principal
- policy coverage
- age, gender, past claims history
- current levels of medical inflation
15
Q
Disadvantages of claim estimates
A
- cannot be used to produce estimates for claims that have not been reported
- relies on skill and judgement of individuals
- assessors may be naturally conservative or optimistic in their assessment
- case estimates are extremely difficult to check
- if estimates used for negotiation with claimants, there may be a tendency for the estimate to be biased to the lower end
- might be thousands of outstanding claims and will take many person-hours in total to estimate each claim amount individually making method very expensive
- assessors may not use consistent rates of inflation
- in some cases, estimates of outstanding claim reserves will need to be made by outsiders who don’t have access to all the data
16
Q
Advantages of claim estimates
A
- only approach that can make use of all known data on outstanding claims
- there are qualitative factors that influence the amount of a claim
- can be applicable when statistical methods are not reliable
17
Q
Statistical estimates
A
- appropriate for particular types of homogeneous claims where the portfolio is large enough and the experience is deemed to be stable.
- outstanding claims estimated en masse in relatively homogeneous cohorts based on historical trends and patterns, adjusted for known or anticipated future changes.
- portfolio is segmented
- statistical distribution is fitted to past experience to estimate the claims incurred from the earned premium
- can incorporate IBNR provision
18
Q
Statistical estimate methods
A
- chain ladder method
- average cost per claim methods
- loss ratio methods
- blends e.g. bornheutter-ferguson
19
Q
Results may differ because:
A
- adjustments for past inflation
- the choice of reported or paid claims
- the choice of claim cohort
- the choice of different development ratios or different grossing up factors
- the choice of exposure and loss ratio to apply
- assumptions about future inflation
- allowance in claims data for:
- claims settlement expenses, hospital discounts, expected reinsurance recoveries
20
Q
Chain ladder method
A
- uses development ratios that are weighted by the cumulative claims from which they arise.
- can be applied to reported incurred claims or to paid claims
21
Q
Assumptions underlying the basic chain ladder method
A
- for each origin year, the expected amount of claims in monetary terms, paid in each development year, is a constant proportion of total claims, in monetary terms, from that origin year.
22
Q
Assumptions underlying the inflation adjusted paid chain ladder method
A
inflation index is applied to past claims data to bring them in line with the latest year and to inflate the projected claims to the expected year of payment.
23
Q
BF method concepts
A
- whatever claims have already developed in relation to a given origin year, the future development pattern will follow that experienced for other origin years
- the past development for a given origin year doesn’t necessarily provide a better clue to future claims that the loss ratio
24
Q
BF approach
A
- determine the initial estimate of total ultimate claims from each treatment month using premiums and initial expected loss ratios
- multiply these estimates by the proportion outstanding
- add these figures to the claims paid to date to give an estimate of the ultimate loss for each treatment month
25
Steps in bootstrapping the chain ladder method
1. calculate the fitted values and residuals for the points in the past (incremental) claims triangle
2. resample from the residuals to produce a pseudo run-off triangle
3. refit the chain ladder model to the new triangle to determine the revised reserve estimate
repeat steps 2 and 3 x99
26
Assumptions underlying bootstrapping the chain-ladder model
- the run-off pattern is the same for each origin year
- 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
27
Potential data problems
1. errors: the incorrect recording of a claim amount - distorts the development factor
2. omissions - likely because of processing delays
3. distortions
28
Causes of distortions
- external influences such as inflation or changes in underlying nature of the risk
- internal influences such as changes in underwriting, claims settlement or recording procedures and reinsurance arrangements
- changes in type of business attracted in each treatment class
- random fluctuations or large claims in a small portfolio
29
Principles of setting statutory or solvency reserves
1. reserves should cover all liabilities arising from a contract
2. reserves should be calculated using a prudent valuation of all future liabilities for all existing products
3. reserves should take credit for future premiums if these are contractually due to be paid
4. the valuation should be prudent and so the basis should contain margins
5. valuation of liabilities should be consistent with valuation of assets
6. appropriate approximisations or generalisations may be allowed
7. the interest rate should be chosen prudently, taking into account currencies, yields and reinvestment yields
8. the demographic, persistency and expense assumptions used should all be prudent but the expenses can be on an ongoing business basis
9. if the valuation method specifies the amount of expenses assumed, then the amount must be no less than a prudent estimate of the relevant expenses
10. the valuation calculations conducted over time should not suffer discontinuities arising from arbitrary changes to the basis
11. the valuation method should recognise the emergence of profits appropriately over the policies' lifetimes
12. valuation bases and methods should be disclosed
30
How to calculate SCR
- VaR: the amount of capital required so that its assets exceeds its liabilities in one year's time with a prob of 99.5%. The supervisory balance sheet is subject to shocks on each of the identified risk factors, at the defined confidence level over the defined period. The surplus is then recalculated at the end of the period.
- calculate capital requirement for each individual risk combine them in such a way that reflects any diversification benefits that exist between the various risks.
31
Market-consistent reserves
To determine liabilities, future unknown parameter values and cashflows are set so as to be consistent with market values, where a corresponding market exists
32
Liquidity premium
Normally restricted to long-term predictable liabilities for which matching assets can be held to maturity. Since the insurer is not exposed to the risk of changing spreads on such assets, it may be permitted to increase the RDR.
33
Market-consistent: mortality and morbidity assumptions
Difficult to obtain market-consistent assumption since there is not a sufficiently deep and liquid market in which to trade or hedge such risks.
The mortality/morbidity assumptions could be determined from the risk premium rates quoted by reinsurance companies
Risk margin included due to inherent uncertainty.
34
Expense assumption
expense assumption could be determined by reference to expense agreements available in the market (from third party admin companies)
risk margin included due to inherent uncertainty.
35
Cost of capital approach for overall reserving margin
1. project required capital at each future time period (amount required in excess of the projected liabilities)
2. multiply the projected capital amounts by the cost of capital
3. discount using market-consistent discount rates to give the overall risk margin
36
Simplified way of projecting required capital
Select a driver which has an approximate linear relationship with the required capital. the initial capital requirement can be expressed as a percentage of the driver, and the projected capital is then approximated as the same percentage of the projected values of the driver.
37
Passive valuation approach
uses valuation methodology that is relatively insensitive to changes in market conditions and a valuation basis that is updated relatively infrequently.
38
Advantages of passive approach
- more straightforward to implement
- involves less subjectivity
- relatively stable profit emergence
39
Disadvantages of passive approach
- at risk of becoming out of date
- insensitive to changes in market conditions and basis is updated relatively infrequently
- may not have taken account of important trends
- management may fail to take appropriate actions in response to emerging problems because solvency position hasn't appeared to change
40
Active valuation approach
- based more closely on market conditions
| - assumptions updated on a frequent basis
41
Advantages of active approach
- more informative in terms of understanding impact of market conditions on ability of company to meet obligations.
42
Disadvantages of active approach
- results are potentially more volatile. Under adverse equity market conditions, an active approach using risk-based capital would indicate that higher capital requirements are needed. To reduce this requirement, they would sell equities - which itself could exacerbate these conditions
- more complex and costly to perform calculations
