Chapter 23 - reserving

Question 1

The purpose of calculating reserves

Answer 1

ARMIC

1. determine liabilities to show in published accounts
2. determine liabilities to be shown in supervisory accounts (if separate accounts have to be prepared)
3. to determine liabilities to be shown in internal management accounts
4. assist with assessment of reinsurance arrangements
5. value the insurer for merger or acquisition
6. influence investment strategy
7. 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

Question 2

Reserves for short-term

Answer 2

• UPR
• URR
• IBNR
• claims in transit
• outstanding claims reserve
• incurred but not enough reported
• equalisation or catastrophe reserve
• investment mismatch

Question 3

UPR

Answer 3

The balance of premiums received in respect of periods of insurance not yet expired

Question 4

URR

Answer 4

• 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

Question 5

Claims in transit

Answer 5

reserve in respect of claims reported but not assessed or recorded

Question 6

Outstanding claims reserve

Answer 6

reserve in respect of claims notified to the insurer but not fully settled

Question 7

IBNER

Answer 7

• reserve for outstanding reported claims

- adjustment to existing outstanding claims reserve

Question 8

Equalisation or catastrophe reserve

Answer 8

reserves where it is felt that the current year and abnormal amounts will have to be held back for abnormal events.

Question 9

Methods to calculate reserves

Answer 9

• case estimates

- statistical estimates

Question 10

when would you use statistical estimates for long-term?

Answer 10

Usually used where benefits are paid as an income

Question 11

When would you use case estimates for long-term?

Answer 11

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)

Question 12

When would you use statistical estimates for short-term?

Answer 12

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.

Question 13

Claims estimates

Answer 13

claims manager inspects claims papers and estimates the ultimate outgo for each case individually

Question 14

What factors for PMI will be taken into account when calculating claims estimates?

Answer 14

1. procedure type
2. hospital to be used
3. name of surgeon, consultant, or other medical principal
4. policy coverage
5. age, gender, past claims history
6. current levels of medical inflation

Question 15

Disadvantages of claim estimates

Answer 15

• 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

Question 16

Advantages of claim estimates

Answer 16

• 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

Question 17

Statistical estimates

Answer 17

• 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

Question 18

Statistical estimate methods

Answer 18

• chain ladder method
• average cost per claim methods
• loss ratio methods
• blends e.g. bornheutter-ferguson

Question 19

Results may differ because:

Answer 19

• 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

Question 20

Chain ladder method

Answer 20

• 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

Question 21

Assumptions underlying the basic chain ladder method

Answer 21

• 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.

Question 22

Assumptions underlying the inflation adjusted paid chain ladder method

Answer 22

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.

Question 23

BF method concepts

Answer 23

• 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

Question 24

BF approach

Answer 24

• 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

Question 25

Steps in bootstrapping the chain ladder method

Answer 25

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

Question 26

Assumptions underlying bootstrapping the chain-ladder model

Answer 26

- 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

Question 27

Potential data problems

Answer 27

1. errors: the incorrect recording of a claim amount - distorts the development factor 2. omissions - likely because of processing delays 3. distortions

Question 28

Causes of distortions

Answer 28

- 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

Question 29

Principles of setting statutory or solvency reserves

Answer 29

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

Question 30

How to calculate SCR

Answer 30

- 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.

Question 31

Market-consistent reserves

Answer 31

To determine liabilities, future unknown parameter values and cashflows are set so as to be consistent with market values, where a corresponding market exists

Question 32

Liquidity premium

Answer 32

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.

Question 33

Market-consistent: mortality and morbidity assumptions

Answer 33

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.

Question 34

Expense assumption

Answer 34

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.

Question 35

Cost of capital approach for overall reserving margin

Answer 35

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

Question 36

Simplified way of projecting required capital

Answer 36

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.

Question 37

Passive valuation approach

Answer 37

uses valuation methodology that is relatively insensitive to changes in market conditions and a valuation basis that is updated relatively infrequently.

Question 38

Advantages of passive approach

Answer 38

- more straightforward to implement - involves less subjectivity - relatively stable profit emergence

Question 39

Disadvantages of passive approach

Answer 39

- 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

Question 40

Active valuation approach

Answer 40

- based more closely on market conditions | - assumptions updated on a frequent basis

Question 41

Advantages of active approach

Answer 41

- more informative in terms of understanding impact of market conditions on ability of company to meet obligations.

Question 42

Disadvantages of active approach

Answer 42

- 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