Reserves

Question 1

What is the main reasons for holding reserves?

Answer 1

• To determine the liabilities for the published accounts of the insurer
• If supervisory requirements, require different bases, to determine liabilities for the solvency accounts of the insurer.
• To determine the liabilities for the internal management accounts
• To value an insurer for a merger and/or acquisition.
• To assist in reinsurance arrangements.
• To influence the investment strategy.

Question 2

What are the different types of short term reserves that are not appropriate for long term business?

Answer 2

Unexpired premium reserve: The balance of premiums received in respect of periods of insurance not yet expired

Unexpired risk reserve: 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 (adjustment to UPR)

Claims in transit: Reserves in respect of claims reported but not assessed, or not recorded (pipeline cases).

OCR: Reserve in respect of claims notified to the insurer but not yet fully settled

Incurred but not enough reported: As above but where it is felt that not all detail has yet been submitted and a provision has to be established for the remainder (adjustment to OCR)

Question 3

When is case estimation more appropriate that statistical estimates?

Answer 3

• When the claims are not predictable or consistent.
• When there are a few claims.
• When the claim case is usually high in value.
• No appropriate statistical model
• New class of business
• Heterogenous claims
• Insufficient data for statistical methods
• High variance in claim amount
• When there is an experience team of claim assessors.

Question 4

What do claim assessors look for in case estimation?

Answer 4

• Doctor or medical professional who performed the procedure/administered the treatment
• The benefit plan the PH was on.
• The type of procedure.
• The hospital/clinic medical treatment was given at.
• The terms and conditions of the policy.
• The age and gender of the policyholder and past history of claiming
• Current level of medical inflation.

Question 5

What are the drawbacks or risks of statistical estimation?

Answer 5

• data used has errors, omissions or distortions , which invalidate the underlying assumptions.
• to fix distortions, users who are aware of the problems can make compensatory adjustments to the data or methods so statistical methods still used
• Reasons for distortions:
  > External influences (e.g. inflation / changes in nature of risk)
  > Internal influences (changes in underwriting, claims settlement / recording procedures)
  > Changes in the type of business attracted, or random fluctuations or large claims in a small portfolio.

Question 6

What is the disadvantages of case estimation?

Answer 6

• Cannot be used to produce estimates for claims that have not been reported(whether incurred or not)
  
  • IBNR must be estimated separately using other methods
• The estimate relies on the skill and judgement of individuals
• Assessors may be naturally conservative or optimistic
• If the estimate is used for negotiation with claimants, there may be a tendency for the estimate to be biased to the lower end
• Case estimates are extremely difficult to check
• Case estimates will take very long and may be very expensive
• Assessors may not use consistent rates of inflation & it will be hard to produce estimates on a range of possible bases
• Cannot use if outsider and do not have access to all the data on individual claims

Question 7

What are the principles of setting solvency reserves?

Answer 7

Now, there’s this big reservoir, with enough water to go around the village. This reservoir has existed for millions of years, and has always been full due to prudent way water is ratioed - guaranteeing water for all. There was never any “best estimate” guesses they rations were always very accurate, and came with a slice of margerine. The method used to calculate ratio was passed down from generation to generation.

• Ensure the insurer has sufficient funds to meet all liabilities
• Based on prudent valuation of future liabilities for all existing policies (include options, guarantees)
• Not a “best estimate” valuation, should include margin for adverse experience
• Insurers should disclose the methods and bases used in the valuation

All the people in the town had big assess and were considered cunty, because of the water. But some were misfits who didn’t drink reserve water at all.

Asset-Liability Management:
- Consider the nature, term, and valuation method of corresponding assets
- Hold a mismatching reserve if there is a mismatch between assets and liabilities

Everyone from the neighbouring town, assumed that the reservoir town people were interesting as they had electric current hair all the time. The demographic was mostly black, but then there was Percy Montgommery too. He worked as an admin clark for COM bank. Usually his expenses were pre-defined by the bank, but if they were not prudent enough he discarded them. Sometimes he needed to consider his expenses if he didn’t buy any new clothes at all.
Assumptions:
- Interest rate: Chosen prudently, considering currency of benefits and yields on corresponding assets
- Statistical basis: Demographic and persistency assumptions selected prudently
- Expenses: Allowance for administrative costs and commissions chosen prudently
- Expenses: If a valuation method predefines expenses, it should not be less than a prudent estimate of future expenses (net premium valuation method)
- Expenses: allowance for expenses, should consider the possibility of the insurer ceasing to write new business

He realised if he did this he could no longer sign up for prophet courses, which would cause discontinuities in his exam progress.
Profit Recognition and Valuation Consistency:
- Method should recognize profit appropriately over the policy duration
- Avoid discontinuities from arbitrary changes to the valuation basis

Question 8

What is the principle of “non-linearity” and “non-separability”?

Answer 8

• Principle of linearity - capital required is a linear function of the risk drivers (in reality = non-linear), e.g. a drop in interest rates (from 5% to 4% vs 5% to 3%) with an option to purchase an annuity at a guaranteed rate of 3.5%
• Non-separability - refers to situations where if two events happen together, the combined impact is worse than if they had happened separately (e.g. longevity risk and expense risk for immediate needs annuities).

Question 9

What is the active vs. passive approach of setting reserve?

Answer 9

Passive
- Uses a valuation methodology that is relatively insensitive to changes in market conditions and a valuation basis that is updated relatively infrequently.
- e.g. Net premium valuation approach for liabilities - fairly insensitive to yield changes due to the net premium also being recalculated under the new assumptions.
Active
- An active approach would be based more closely on market conditions, with the assumptions being updated on a frequent basis.
- e.g. The use of market-consistent valuation approaches for both assets and liabilities, and risk-based capital approach to SCR.

Question 10

What are the pros and cons of passive approach?

Answer 10

• Advantages:
  
  • More straightforward to implement, involves less subjectivity and result in relatively stable profit emergence.
• Disadvantages:
  
  • Passive valuation is at risk of becoming out of date.
  • If the stock market crashes, the assets will be overvalued.
  • If the valuation basis is changed infrequently, it may not take account of important trends e.g. rising inflation / deteriorating claims experience. So, there is a danger that a passive valuation approach provides a false sense of security.
  • SCR may be determined using a simplified approach such as holding a prescribed % of best estimate liabilities.

Question 11

What are the pros and cons of active approach?

Answer 11

• Advantages
  
  • More informative i.t.o. understanding the impact of market conditions on the ability of the company to meet its obligations (particularly for financial guarantees & options).
• Disadvantages
  
  • Results are potentially more volatile.
  • Under adverse equity market conditions, an active valuation approach using risk-based capital would indicate that higher capital requirements are needed. To reduce this -> sell equities, which could exacerbate the market conditions.
  • There is also a systemic risk - as this would be the case for all health and care insurance companies at the same time.
  • Regulators may include amendments to the valuation approaches under such conditions to avoid this situation.
  • Active valuation approach -> more complex than a passive approach -> calcs take longer and more costly

Question 12

What is the interplay between solvency reserves and solvency capital requirements?

Answer 12

• Supervisors will require that an insurer maintains at least a specified level of solvency capital in addition to the reserves or technical provisions held
• Provides an additional level of protection to PHs (of reserves being underestimated & a drop in asset values)
• The level of SC required under regulation:
  
  • Could be specified as formula e.g. SC is 3% of reserves
  • Could be based on risk measure
  • Example SC is 3% of reserves (cover fall in assets) and 0.3% of sum at risk (cover bad mortality experience)
• Adequacy of reserves and SCR cannot be looked at in isolation.
• Reserves may be set up on a relatively realistic basis (small margins) with a requirement for a substantial level of SC determined using risk-based capital techniques.
• Reserves may be set up on a prudent basis (large margins) with a relatively small SCR that is not specifically related to the risks borne by the company

Question 13

For which health products are reserves very important and why?

Answer 13

Reserves are very important for pre-funded long term care products because of the mismatch in timing between when premiums are received and when benefits are paid.
When the policyholder is in different stages, this determines the level of reserves that need to be held at the time.
When an individual dies, they are no longer claim and the reserves are released.
Higher reserves are required for individuals who are in the claim state vs. individuals who are in the healthy stage.

Question 14

How do you design products that are capital efficient?

Answer 14

• Try to match income and outgo as closely as possible e.g. use level commission for level premium products.
• Use unit-linked designs as capital efficiency can be achieved through low allocation rates in beginning etc.
• Try and avoid guarantees and options.
• Avoid innovative products which regulators neem risky.
• Use best data to price premium and calculate reserve to reduce uncertainty in parameters
• Limit extent of uncertainty surrounding benefit payout e.g. no indemnity and strict claim definitions.

Question 15

How does OCR reserve factor into total claims paid calculation?

Answer 15

Total claims incurred in 2009 = Total claims paid in 2009 + increase in OCR during 2009
OCR represents claims which have been reported but not yet settled.
We add OCR at end of 2009 as, there claims were incurred in 2009, but have not yet been paid.
We subtract OCR at end of 2008, as these claims were incurred in 2008, but only settled in 2009.
Increase in OCR during 2009 =OCR as at 31 December 2009 - OCT as at 31 December 2008
Some of the claims paid in 2009, were for claims incurred in 2008

Question 16

What reserves are needed for annual premium critical illness policies?

Answer 16

*Overall the reserves will be quite small for critical illness because claims are only paid on diagnosis of CI which is rare.

Policy reserves is discounted value of future claims and expenses less premiums
* Will be the majority of the CI reserves
* Policy reserves + premiums are held to meet benefits paid out in the future.
Claims reserve is EPV of claims + EPV of expenses
* Includes IBNR claims that have been diagnosed but not reported (could be big if claims take a well to be reported)
* Include IBNS claims that have been diagnosed but not settles (should be small unless delay in claim payments)
Option reserves are additional cost that need to be set aside if option comes into the money in the future
* Include option to increase sum assured or term of the policy

Question 17

How can solvency capital required be calculated using VaR approach?

Answer 17

1. Identify risks: The insurer identifies the various risks it faces, such as underwriting risk, market risk, credit risk, and operational risk.
2. Stress test each risk: The insurer stress tests each risk factor in isolation, using a defined confidence interval (e.g., 99.5%) and time period (e.g., one year). This reveals the capital required to withstand adverse scenarios for each risk. There are different ways to define the time horizon and the confidence level used in the calculation
3. Aggregate capital requirements: The insurer then aggregates the capital requirements for each risk to determine the total capital needed. This is typically done using correlation matrices or copulas, which account for the relationships between risks. The aggregate capital requirement is usually less than the sum of individual risk capital requirements due to diversification benefits.
4. Adjust for non-separability and non-linearity: The insurer adjusts the aggregate capital requirement to account for situations where the combination of events happening simultaneously may produce a higher capital requirement than combining them using a correlation matrix (non-separability) or where the capital required is a non-linear function of the risk drivers.
5. Use stochastic models: Insurers typically use stochastic models to quantify the capital requirements for economic risks. These models should capture the extreme behavior of the variables being modeled.
6. Calibrate models to historical data: The models used for capital requirement projections should be calibrated using historical parameters to ensure they accurately reflect real-world conditions. Advanced techniques may be needed to ensure the models appropriately fit the tail of the distribution and do not understate the frequency of extreme outcomes.

The VaR approach helps insurers determine the amount of capital they need to hold to ensure they can meet their obligations with a high level of confidence, even under adverse conditions. The solvency capital requirement is an essential aspect of an insurer’s risk management and financial stability.

Question 18

What are the different ways to define the time horizon and the confidence level used in the calculation of solvency capital in VaR approach?

Answer 18

1. Minimum required confidence level over a defined period:
   
   • In this method, the insurer calculates the amount of capital needed to ensure that its assets exceed its liabilities (A > L) over a specified time period (e.g., one year) with a given probability (e.g., 99.5%).
     Used in Solvency II
2. Run-off method:
   
   • The run-off method takes a longer-term view and considers the amount of capital needed at the outset to ensure the insurer can cover its liabilities until the last policy has expired or been settled.

Question 19

What are important concepts regarding market consistent reserves?

Answer 19

• Illiquidity premium
• Risk margin

Question 20

What is method of market consistent reserve calculation?

Answer 20

• market consistent reserve = the price that someone would charge for taking responsibility for the liability, in a market in which such liabilities are freely traded.
• Future unknown parameters and cashflows are set so as to be consistent with market values, where a corresponding market exist
• Could devise a replicating portfolio of assets whose cashflows exactly replicate those of the liabilities, and then the current market price of this is the market-consistent value of the liabilities
  e.g. expected cashflow on an immediate needs LTCI contract - can value the cashflows of a series of zero coupon “risk-free” bonds of matching terms
• Assumed future investment returns (and discount rates) are based on the risk-free rate of return
• “risk-free” rates may be determined based on government bond yields or on swap rates
• It may be appropriate to make a (as they are not entirely risk-free) deduction to allow for credit risk
  
  • Generally only appropriate to use swap rates if there is a sufficiently deep and liquid swap market in that country
• Market-consistent valuation methods have been increasing in importance in some countries.

Question 21

What is an illiquidity premium?

Answer 21

• The illiquidity premium is the extra return that investors require to compensate them for the risk of greater price volatility of an asset.
• sometimes you can add illiquidity premium to risk free rate in order to discount resulting in lower reserve amounts
• only possible for long term liabilities (if short term, there is still liquidity risk)
• matching asset must be held to maturity, or else still at risk of liquidity issues
• usually strict rules about how and when illiquidity premium can be applied

Question 22

What is a risk margin and when is it applied?

Answer 22

• The risk margin is meant to reflect the compensation the market requires for taking on uncertain aspects of liability cashflow.
• Could add a risk margin to individual assumption that you are uncertain about e.g. mortality assumption.
• Could calculate an overall risk margin calculated using cost of capital approach.

Question 23

Describe how best estimate and solvency reserves can change the profit/loss made by new written policy

Answer 23

Say the best estimate reserve is -10 and the solvency reserve is 30
The premium is 80 and profit margin is 25
First premium income less initial expenses is 15.
When company writes new policy under best estimate assumptions, A increases by 15 and reserves decrease by 10, thus total surplus of R25 - this is in line with profit margin.
When company writes new policy under solvency assumptions, A increases by 15 and reserves increase by 30, thus total surplus decreases R15 - this is considered new business strain and premium clearly insufficient to meet reserves and initial expenses.

Question 24

What are the assumptions of the Bornhuetter-Ferguson method?

Answer 24

• Payments from each origin will develop in the same way
• No explicit assumptions are made for claims inflation
• The estimated loss ratio is appropriate
• The development factor to ultimate is never less than 1
• The first year is fully run off.

Question 25

Bornhuetter-Ferguson method: Why is development factor to ultimate never less than one?

Answer 25

• A development factor of 1 means that the claims are fully developed, and no further growth is expected.
• A development factor greater than 1 indicates that the claims are expected to grow further before reaching the ultimate loss.
• A development factor less than 1 would imply that the ultimate loss is less than the current reported loss which doesn’t make sense.

Question 26

What is bootstrapping?

Answer 26

• A technique for determining the the statistical properties of a quantity
• It uses the randomness in a sample from an underlying population and applies the Monte Carlo approach
• It involves sampling (with replacement) repeatedly from an observed data set to create a number of pseudo-data sets.
• Various statistics of interest can be derived from each pseudo-data set. Use BCL to determine IBNR reserves for each set.
• The distribution of these statistics can be analysed further.
• It is assumped that the sampled data are independent and identically distributed.
• In stochastic claims reserving, bootstapping techniques can be used to estimate distribution of IBNR reserves rather than just a point estimate.

Question 27

How is bootstapping used with reserve protections?

Answer 27

• Get a set of past claim data, split by origin year.
• Back-fit a model to the past data to find the expected claims for each cell.
• Calculate the residual “noise” present in each cell i.e. actual claims less expected claims.
• Sample from this residual distribution to produce many pseudo-data sets.
• Calculate the reserve protections based on each psedu-data set.
• Collate the reserve projections to determine the distribution, moments and percentile of reserve distribution.

Question 28

When will a risk margin be applied?

Answer 28

• Sometimes market-consistent assumptions do not exist for certain risks within the market
• Examples include: mortality, persistency and expense risks.
• This is because the market is not sufficiently deep and liquid to trade or hedge such risks.
• We could look at risk premium rates quotes by reinsurers for mortality assumptions but this takes long and likely won’t be given freely.
• To combat this, we can add risk margins to assumptions to reflect uncertainty.

Question 29

How is overall risk margin calculated?

Answer 29

1. C_t: Project required capital at each future period (amount required in excess of projected liabilities)
   * can be complicated e.g. use stochastic models
   * can use % of driver which has linear relationship with required capital e.g. reservers or sum at risk
2. Multiply cost of capital rate (k_t) by protected required capital amounts (C_t)
   * k_t represents the frictional cost to the company of locking in capital to earn risk free rate rather than being able to invest freely
   * k_t represents cost of raising incremental capital in excess of risk free rate.Can be determined as excess of weighted average cost of capital over risk free rate.
   *sometimes k_t is a specified rate e.g 6% in Solvency II
3. Discount this product using risk-free interest rate for maturity t to get the risk margin for each future period i.e. (1+r_t)^-t
4. Sum over all future periods to get the overall risk margin.

Question 30

Why is IBNER a seperate reserve?

Answer 30

• Might have different trends, so better to model seperately
• Might be taxed differently so better to model seperately
• Gives management more information to be able to make decision

Question 31

What is the list of different reserves?

Answer 31

• IBNR reserve: claim incurred but insurer not notified.
• Claims in transit: insurer notified but no assessment by insurer.
• Outstanding claims reserve: insurer notified but claim not fully settled
• IBNER reserve (+ (or -) to OCR): feel like not all detail submitted so make provision for remainder.
• Unearned premium reserve: prospective approach to ensure reserve kept for risk not expired.
• Unexpired risk reserve (+ (or -) to UPR): retrospective approach, where extra reserve held if premiums insufficient to meet future claims and expenses.
• IBNS reserve: LTC claims in payment or CI in assessment.
• Policy reserve: EPV (claims+expenses-premiums)
• Option reserve: if option bites
• Mismatching reserve: if assets and liabilities are not well matched.
• Equalisation reserve: funds in profitable years for less profitable years i.e. smooth profits.
• Catastrophe reserve: funds held incase future catastrophe happens
• Active life reserves: for IF policies, that haven’t claimed benefits.
• Claim reserves: reserves set aside for approved claims that have not yet been fully paid out i.e. disabled life reserves.

Question 32

Why are certain reserves not applicable to LTC insurance but are to PMI.

Answer 32

• claims in transit (processing): not applicable if there are ongoing payments as there will be no processing delay.
• URR and UPR: LT premiums are priced to be sufficient to cover expected claims over policy duration - this reserve more relevant for ST non-level premiums where risk + premium not evenly distributed over term.
• outstanding claims reserve (payment) : these claims are already defined so no significant delays to settle the claim
• catastrophic reserve: no need because of pre-defined event, so not subject to fluctuations in claim cost thus no need to reserve.

Question 33

Assumptions for basic chain ladder method

Answer 33

• payments from each origin year will develop in the same way in monetary terms
• past inflation will continue into the future.
• the first year is fully run off

Question 34

Assumption for the inflation-adjusted chain ladder

Answer 34

• payments from each origin year develop the same way in **real **terms
• rates of past and future claims inflation is appropriate
• future inflation is not automatically allowed for but is input into the model
• the first year is fully run off