What is the main reasons for holding reserves?
- 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.
What are the different types of short term reserves that are not appropriate for long term business?
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)
When is case estimation more appropriate that statistical estimates?
- 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.
What do claim assessors look for in case estimation?
- 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.
What are the drawbacks or risks of statistical estimation?
- 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.
What is the disadvantages of case estimation?
- 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
What are the principles of setting solvency reserves?
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
What is the principle of “non-linearity” and “non-separability”?
- 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).
What is the active vs. passive approach of setting reserve?
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.
What are the pros and cons of passive approach?
- 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.
What are the pros and cons of active approach?
- 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
What is the interplay between solvency reserves and solvency capital requirements?
- 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
For which health products are reserves very important and why?
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.
How do you design products that are capital efficient?
- 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.
How does OCR reserve factor into total claims paid calculation?
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
What reserves are needed for annual premium critical illness policies?
*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
How can solvency capital required be calculated using VaR approach?
- Identify risks: The insurer identifies the various risks it faces, such as underwriting risk, market risk, credit risk, and operational risk.
- 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
- 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.
- 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.
- 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.
- 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.
What are the different ways to define the time horizon and the confidence level used in the calculation of solvency capital in VaR approach?
- 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
- 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%).
- 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.
What are important concepts regarding market consistent reserves?
- Illiquidity premium
- Risk margin
What is method of market consistent reserve calculation?
- 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.
What is an illiquidity premium?
- 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
What is a risk margin and when is it applied?
- 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.
Describe how best estimate and solvency reserves can change the profit/loss made by new written policy
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.
What are the assumptions of the Bornhuetter-Ferguson method?
- 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.
