Chapter 23 Reserves & solvency capital requirements

Question 1

Types of reserves:Short-term

Answer 1

• 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

Question 2

The role of statistical and case estimates:Long-term

Answer 2

• 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.

Question 3

The role of statistical and case estimates:Short-term

Answer 3

-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.

Question 4

Statistical estimates

Answer 4

• 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.

Question 5

Basic chain ladder assumptions

Answer 5

• 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.

Question 6

The Borhhuetter Ferguson method merits

Answer 6

• 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 crude us of a loss ratio by taking into account information provided by latest development.

Question 7

Assumptions underlying the Bornhuetter Ferguson method

Answer 7

• 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.

Question 8

Steps in calculating a reserve using BF method.

Answer 8

• 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.

Question 9

Explain boostrapping and what it is used for?

Answer 9

• 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.

Question 10

Weakness of statistical methods

Answer 10

• 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.

Question 11

Assumptions underlying bootstrapping the BCL

Answer 11

• 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.

Question 12

Distortions in data and results can occur due to a number of reasons

Answer 12

• 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.

Question 13

Discuss the need for solvency capital

Answer 13

• 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.
  1. Against drop in asset values
  2. Against adverse experience relative to that assumed in reserves
• The level of SCR under regulation may be specified as a formula or it may be based on a risk measure such as VaR.

Question 14

Interplay between reserves and SCR

Answer 14

• 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.

Question 15

Value at Risk approach

Answer 15

• 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.

Question 16

Other possible methods

Answer 16

• 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.

Question 17

Combining separate risks will lead to higher SCR than if if risks were combined using diversification matrices. What causes this?

Answer 17

• non-linearity

- non-separability of individual risks

Question 18

What is linearity?

Answer 18

-the capital required is a linear functions of the risk drivers.

Question 19

What is non-separability?

Answer 19

-refers to situations when if two events happen together, the combined impact is worse than if they happened separately.

Question 20

Market-consistent reserve methodology

Answer 20

• 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

Question 21

Market-consistent: Illiquidity premium approach

Answer 21

• 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.

Question 22

Market-consistent: Risk margin

Answer 22

• 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.

Question 23

Describe the cost-of-capital approach to calculating the risk margin

Answer 23

• 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.

Question 24

What is an active valuation approach?

Answer 24

-it is based more closely on market conditions with assumptions being updated on a frequent basis.

Question 25

Advantages of using a passive valuation approach?

Answer 25

• 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.

Question 26

What is an active valuation approach?

Answer 26

-it is based more closely on market conditions with assumptions being updated on a frequent basis.

Question 27

Disadvantages of using passive valuation approach

Answer 27

• 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.

Question 28

Advantages & disadvantages of active valuation approach

Answer 28

+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