Chapter 18: Reserving uncertainty

Question 1

Best estimate reserve definition and Characteristics of a best estimate reserve

Answer 1

“Best estimate is a point estimate and does not convey a range of estimates.
It is prepared by actuaries using statistical or other established actuarial techniques or practices
When arriving at a best estimate, we do not deliberately add any margins or prudence or adjust to get a optimistic value.
Actuaries endeavor to prepare it without any bias or favor for a particular method/approach.
However, it includes any current information that is relevant for the claims.
“

Question 2

Four approaches to quantify uncertainty as per TAS R

Answer 2

“The four approaches are:
• giving a range, measure of the value at risk or other statistical calculation
• showing the numerical consequences of changes in assumptions
• presenting the outcomes of scenarios, possibly including extreme scenarios
• describing the uncertainty and explaining why it has not been quantified.”

Question 3

Points to consider when reporting uncertainty

Answer 3

“The key points to consider when communicating the uncertainty in reserve estimates are:
• A numerical estimate of uncertainty should be included in any formal report that gives a point estimate of reserves.
• Relevant professional guidance should be adhered to …
• … eg TAS R states that an actuarial report “shall indicate the nature and extent of any material uncertainty in the information it contains.”
• Consider whether it is practical to quantify the uncertainty …
• … often expressed in percentiles …
• … or whether on it is sufficient to include a descriptive summary.
• Note that a percentile approach is a percentile within a model and is therefore prone to residual model error.
• Consider the need to demonstrate the uncertainty in outcome rather than a range for the best estimate.
• Consider need to communicate uncertainty in a way that the intended audience will understand …
• … consider their level of technical knowledge.
• It is likely that stakeholders will prefer being told the range of possible outcomes.”

Question 4

A2021 - Q3:
(i) Suggest possible reasons why a general insurance company may wish to
include a loading on top of its best estimate reserves.

Answer 4

(i)
To allow for potential adverse experience that the Company may suffer [½]
Such that reserves are not exhausted when experience is worse than expected [½]
May be a regulatory requirement [½]
Maintain/improve credit rating [½]
Stay in line with competition [½]
Most candidates seemed to understand the Use test well, although a few candidates did appear to think of calculating the capital itself being the main component of the Use Test.

Perhaps because the company has always done so, and to keep it consistent with the past practice [½]
Provide higher level of confidence to the various stakeholders in the company’s ability to meet claims to various stakeholders [½]
To allow for sufficient prudence in the reserves as per the accounting principle of prudence [½]
Best estimates might only be the central estimate of the loss distribution, and may not be fully representative of the actual performance which can be more adverse [½]
Historical experience of late reporting of losses/ large losses causing the Best Estimate to being insufficient [½]
Management decision based on their understanding of the business [½]
Smoothing of results year-on-year [½]
Deferring profits or tax management [½]
Changes to the claims handling policies rendering case reserves being booked at the lower end of the spectrum

Question 5

A2021 - Q3:
A large personal lines insurer mainly writes Household insurance business.
Historically, the insurer has booked the Chief Actuary’s best estimate reserves.
However, the insurer is now considering adding an additional margin for uncertainty
on top of the best estimate reserves.
(ii) Describe three possible approaches that the company may take to calculate
such a margin for uncertainty. [6]
(iii) Discuss the advantages and disadvantages of each of the approaches in
part (ii).

Answer 5

(ii)
Percentile-based approach/Stochastic approach
Set Margin for Uncertainty (MfU) to bring reserves up to a certain percentile, e.g. up to 75th percentile [1]
Involves coming up with a distribution of the reserves [½]
Stochastic approach to setting the MfU. [½]
Mack/ODP [½]
Scenario-based approach
Process of setting the MfU based on certain specified real-life scenarios around companies’ reserve estimates [1]
Typically involves considering possible events that could have an adverse impact on companies’ reserves [½]
Can derive a scenario in a variety of ways: basing it on an historical event, thinking up a hypothetical event using our judgement, or from the results of a stochastic model [½]
Based on the concept that in extreme conditions, areas of uncertainty may become more correlated [½]
For example, risk of fires and subsidence claims during and following a spell of dry weather [½]
Any other suitable examples, including the ones in the Core reading [½]
Percentage loading on top of best estimate
Simply involves applying a straight percentage loading on top of companies’ best estimate reserve picks [1]
Percentage arrived at using judgement [½]
Or could be prescribed by the regulator [½]
Cost of Capital approach
Involves calculating an explicit MfU as a risk margin calculated using a cost of capital approach, where future projected capital requirements are multiplied by a chosen cost of capital % [1]
The cost of capital may be prescribed by the regulator, or industry practice [½]
SP7 - General Insurance - Specialist Principles - April 2021 - Examiners’ report
SP7 A2021 © Institute and Faculty of Actuaries
and then discounted back to the present day [½]
Ad-hoc loading approach
Involves adding an explicit ad-hoc loading amount on top of the best estimate reserves, [1]
For example, $Xm on top of best estimate [½]
Typically arrived at using judgment [½]
Could represent a loading for estimates for a 1-in-200 flood event [½]
Alternative set of assumptions
Involves choosing an alternative, more prudent set of assumptions compared to the actuary’s best estimate view, [1]
Typically arrived at using judgment. [½]
For example, choosing a slower LDF, higher IELR, more prudent frequency and severity. [½]
If the candidate has provided more than three approaches, mark the best three only since the

(iii)
(iii)
Percentile-based approach
Advantages:
Sophisticated approach that is consistent year-on-year [½]
Specified valuation approach, assists with conversations with Auditors, regulators, etc. [½]
Disadvantages:
Time consuming/Expensive [½]
Complex/difficult to explain [½]
May lead to spurious accuracy, and/or give a false sense of security [½]
Choice of model might not be correct [½]
Impractical if limited past data is available [½]
Scenario-based approach
Advantages:
Takes into account specifics of companies’ exposures to certain scenarios [½]
Because it is aimed at the specific question, we can construct a scenario test and produce reliable results much more quickly than for a stochastic model [½]
Encourages engagement with stakeholders from other areas of the business (e.g. Underwriting, Claims, etc.) as scenarios are easy to communicate and understand [½]
Model uncertainty is much less of a problem when we construct scenario tests because we consider the driving factors explicitly [½]
Disadvantages:
Time consuming to arrive at scenarios and select appropriate probability, many different stakeholders may want to get involved in the process [½]
Significant amount of judgement likely to be involved, both in arriving at possible scenario losses, and in the selection of the likelihood of the scenarios [½]
Typically only give information on the extremes of the distribution of eventual outcomes [½]
Percentage loading on top of best estimate
Advantages:
Simple approach that is easy and inexpensive to update each valuation [½]
May allow greater Board/stakeholder engagement with MfU due to the simplicity of the technique [½]
Disadvantages:
Might be the only option if prescribed by the regulator [½]
May be overly simplistic and hence not allow for specifics of the reserve risks companies are actually exposed to [½]
Arbitrary approach may cause issues in discussions with stakeholders [½]
Difficult to choose a percentage if not prescribed [½]
Cost of Capital approach
Advantages:
Sophisticated approach that is consistent year-on-year [½]
May be reasonably accurate proxy in terms of what the MfU in intended to allow for [½]
Disadvantages:
• Complex/Time consuming [½]
• Expensive/Difficult to explain. [½]
• May lead to spurious accuracy, and/or give a false sense of security. [½]
Alternative Set of Assumptions
Advantages:
Simple to understand [½]
Doesn’t require any additional modelling as the same model can be re-run using a different set of assumptions
Disadvantages:
Choosing the alternative set of assumptions can be tricky [½]
Might not be able to communicate what the statistical level of confidence is for the new outcome, as it doesn’t produce a full distribution [½]
The alternative set of assumptions may require some underlying statistical analysis to arrive at leading to extra effort, and a statistical approach might be better [½]
Ad-hoc loading approach
Advantages:
Simple approach not requiring extensive process [½]
May be reasonably accurate proxy in terms of what the MfU in intended to allow for in that it makes use of expert judgement to feed into estimate [½]
Disadvantages:
Not a structured calculation process, hence incremental process to update each year [½]
May attract attention from Auditors/Regulators as to why there isn’t a structured calculation process around the loading year-on-year [½]

Question 6

From your memory of earlier in the course, write down as many factors as you can that contribute to reserve uncertainty.

Answer 6

Sources of process error 
– – – 
general claims uncertainty –
inherent uncertainty in individual claims (amount, frequency and timing) changes in mix of business demand surge
normal retirement

internal sources, such as: –
– – – –  changes in business mix booked reserves different to best estimate
uncertainty over commission and other sales-related expenses new markets
new types of investment

systematic sources, such as
the economic environment the insurance cycle
The

Sources of parameter error 
the data used –
– – 
poor quality data inconsistent data
incomplete and non-existent data
incorrect modelling assumptions, eg: –
–  
correlations in the model statistical distributions
change in case estimate reserving philosophy planned or unplanned changes in mix

particularly large / unusual risks: –
– –    
large claims catastrophes
latent claims
inadequate data supplied by third party claims handlers format of data
claims inflation not as expected uncertain sales-related expenses, commission, new distribution channels, etc.
Sources of model specification error 
model error   programming error simulation error / too few simulations

Question 7

Model uncertainty in reserving

Answer 7

Model uncertainty is the risk that an inappropriate model has been used in the estimation process.
This arises because actuarial models are often a simplification of a very complex (and unknown) underlying system. By using a simplified model to project the true underlying system, we are introducing an unknown bias into the model.
This introduces uncertainty in the estimates produced by the model.
A common example of this in actuarial modelling is the use of parametric distributions for outstanding claims reserves (like the log-normal distribution). The complexity of the claims process and the factors influencing it make it unlikely that the real distributions match simple statistical models.
We can reduce model uncertainty by using actuarial judgement when we select a model. This means that we select models which best capture the key features of the process. This is especially important when the volumes of past data are insufficient to test whether a model is inappropriate.
For example, by splitting data into perceived homogenous groups, we can reduce model error, but this could also affect the estimates of parameter uncertainty (including correlation parameters) and process uncertainty.
This is because the homogeneous groups may not contain sufficient credible data, therefore increasing uncertainty.

Question 8

Parameter uncertainty in reserving

Answer 8

Parameter uncertainty refers to the uncertainty in determining the parameters for an actuarial model. This usually results from the statistical variability present in the historical data used to estimate the parameters. Past data will never comprise all possible outcomes.
An absence of large losses in historical data can lead to an error in the estimation of the ‘average’ claim development pattern.
For example, mortgage indemnity guarantee business can have long periods of stable (and low) claims experience during periods when the economy is performing well. However there is always the risk of an economic downturn and a significant increase in claims.
If we assign our parameter values by analysing past claims experience only, this will lead to inappropriate reserve estimates.
We can sometimes reduce parameter uncertainty by using judgement when we select parameters. Quantifying the impact of using judgement on parameter uncertainty is itself (usually) a matter of judgement. There will always be some parameter uncertainty.
In combination, parameter and model uncertainty lead to the statistical risk that the outcome of the exercise will not form a good reflection of the underlying claim distribution. This is a result of insufficient / inaccurate data and an inappropriate fit of the model.

Question 9

Process uncertainty in reserving

Answer 9

If a process is assumed to be inherently stochastic, the future outcome will be uncertain because of the randomness of the process and the fact of course that many of these events have yet to occur.
This uncertainty is present even if model selection is perfect and the parameters are known with certainty.
An example of this is the uncertainty present in an unearned premium reserve for business exposed to Gulf of Mexico hurricanes. In this case, the eventual liability could be very different from a correct average liability if a hurricane materialises during the unexpired risk period.
This is because there is uncertainty in the timing of the hurricane, related to seasonality, so estimating UPR at a point in time is tricky.
These sources will contribute to the overall uncertainty of a point estimate. The most significant source of uncertainty will depend on the situation.
For example, a key source of process uncertainty for product liability business will be the emergence or otherwise of a new type of claim, whereas for a commercial fire portfolio it might be the occurrence of a major catastrophe.
The process uncertainty in a large portfolio of (reasonably) independent personal motor risks can be quite small compared to model and parameter risk. The opposite might be true for a small book of excess liability risks.
The

Question 10

estimation or prediction error.

Answer 10

We sometimes refer to the combination of process and parameter uncertainty as estimation or prediction error.

Question 11

The process uncertainty in a large portfolio of (reasonably) independent personal motor risks can be quite small compared to model and parameter risk. The opposite might be true for a small book of excess liability risks.
Justify why?

Answer 11

For a small book of business we would expect there to be greater uncertainty surrounding the future outcome.
Also liability business may be more likely to include large heterogeneous risks and have the chance of latent claims emerging. Again this leads to greater uncertainty regarding the future claims outgo, ie increased process uncertainty.
Excess business is likely to be more volatile since it captures only the upper portions of the insured losses and of course the tail-end of any distribution is subject to a high degree of uncertainty.
Further volatility in claim amounts is introduced if different levels of excess apply to each inwards risk.

Question 12

What is a best estimate?

Answer 12

We normally define the best estimate as the actuary’s view of the mean or expected value (also called the unbiased probability – the weighted average) of the eventual outcome.
It is very important to recognise that in many, if not most, situations it will not be possible for the actuary to derive the mean of the outcomes with a high degree of certainty.
Instead, the actuary will estimate a reserve value using an approach that is intended to derive a mean or expected outcome. The actuary will not be certain that the value derived does equate to a mean value but will ascribe the term ‘best estimate’ to the determined value to convey the ‘type’ of estimate that the actuary is deriving.
The term ‘best estimate’ is used in this case to distinguish it from a prudent or optimistic estimate.
In such circumstances, we can consider the best estimate as the actuary’s subjective derivation of the probability-weighted mean of all possible outcomes, taking into account all available information about the business being analysed.
It should also be noted that the actuary will be calculating a sample mean as an approximation to the population mean. This means that a best estimate should allow for information that is available to the actuary but may not be reflected in the underlying data yet.
For example, an actuary may be aware that a portfolio is exposed to catastrophic events, even though no catastrophes have occurred within the period of the past data. Therefore, the actuary will need to make an allowance for this in his/her calculation of the best estimate.
The term ‘best estimate’ reserve is also used in other areas and is not necessarily defined in a statistical framework. For example, under the Solvency II regime, the reserving actuary is required to identify ‘best estimate’ reserves, which are the mean of all possible outcomes, not just those present in the data.

It should be noted that if certain outcomes have been excluded when making the estimate (for example the failure of reinsurance, the emergence of extreme outcomes or latent claims), the estimate will be different than if they had been included. The actuary should make clear what has and what has not been included in deriving the best estimate.
For a point estimate, alternatives to a best estimate are: 
 
the median the mode
an estimate with a particular likelihood of exceeding the outcome.

Question 13

What are the key characteristics of Best Estimate reserves?

Answer 13

The key characteristics of a ‘best estimate’ in this context are that: 

It is a point estimate. The best estimate is described as a single number, not as a range of reasonable outcomes.
It is not inherently optimistic or pessimistic. The best estimate does not include any deliberate bias in the setting of the underlying assumptions. It is meant to be the actuary’s impartial view of the reserves with no margins, implicit or explicit, for prudence or optimism.
 
It is based on sound and appropriate actuarial or statistical techniques. It is based on current and credible information.
The requirements say nothing about the skewness of the underlying distribution or its inherent volatility.

Question 14

3 pillars of solvency II

Answer 14

Solvency II is the regulatory regime applicable to UK general insurance companies in the EU. It requires firms to value their assets and liabilities on a market-consistent basis and more risk-sensitive capital requirements address asset as well as liability risks. It consists of three ‘pillars’.
Pillar 1 sets out the reserving basis and the capital requirements companies are required to meet for insurance, credit, market and operational risk. Capital requirements may be calculated using a standard formula or, if firms have supervisory approval, they may use their own capital models.

Pillar 2 consists of a supervisory review process to evaluate the adequacy of capital and the company’s risk management systems and processes. Supervisors may decide that a company should hold additional capital against any risks not adequately covered in Pillar 1.
The aim of Pillar 3 (disclosures) is to harness market discipline by requiring firms to publish certain details of their risks, capital and risk management.

Question 15

Give examples of insurance risk, credit risk, market risk and operational risk for a household property insurer.

Answer 15

Insurance risk – poor weather, leading to many claims from flooding and burst pipes.
Credit risk – this is the risk of third party default, eg failure of a reinsurer / broker, failure of assets. Market risk – volatility of assets and liability values.
Operational risk – this is the failure of people, processes and systems, eg poor claims handling procedures.

Question 16

Margin in reserves on top of the best estimate:
Risk margin and range

Answer 16

Depending on the purpose, most reserving exercises involve deriving a ‘best estimate’ of the reserves or an alternative estimate that may contain a margin. In other words, the strength of the basis will depend on the purpose of the exercise.
We can see that the best estimate is not a single defined amount that can be derived from a given dataset.
For example, if we gave 100 actuaries the same data and asked them to derive their best estimate of the reserves, the results would not all be the same – in fact there would be a ‘range of best estimates’.
We can define such a range as one which reflects the parameter uncertainty and model error alone; in other words it expresses the uncertainty arising from the selection of parameters and/or a given model, given the data available.
If we asked one of these 100 actuaries to provide an indication of the uncertainty that exists around their selected best estimate (derived using a chosen model or process), this would reflect some or all of the process uncertainty alone.

Question 17

Examples of reserve ranges used by actuaries

Answer 17

1. Range of best estimates
2. ‘Range of possible outcomes’: this would represent the actuary’s estimate of the complete range of outcomes for future claims. It would therefore be significantly wider than the range of best estimates and rarely of much practical use for live portfolios.
   This is because it includes extreme events which might not even be considered as plausible, for example a ‘one-in-1000-year-event’.
   It can be of value as a run-off portfolio nears closure as it becomes important to understand residual uncertainty.
3. ‘Range of reasonable / probable / plausible outcomes’: this would typically be wider than a range of best estimates, but much narrower than the range of possible outcomes.
   It would be wider than a range of best estimates because it would allow for outcomes that cannot be reasonably regarded as an estimate of the mean or average outcome, but which can still be regarded as plausible outcomes.
   We can think of this range as allowing for parameter / model uncertainty and some element of process uncertainty as well. It would effectively include the outcomes that the actuary regards as plausible or probable but exclude those outcomes that the actuary regards as extreme (being either very low or very high). It would exclude the very extremes that would be included in a range of possible outcomes (in general this would not include the possibility that no further claims are paid).

Question 18

Why are such reserve ranges useful?

Answer 18

A range of best estimates or a range of reasonable outcomes may be useful when management are considering what reserve estimates should be booked in their accounts. A range of possible outcomes may be useful when considering the resilience of the company to adverse events and/or when purchasing reinsurance.

Question 19

Estimating the range of possible outcomes

Answer 19

There are methods that allow us to quantify some of the uncertainty in the outstanding reserves. However, we should use judgement when we interpret the results of such methods, just as we do for methods which only produce point estimates.
There are no universally-agreed standards for quantifying uncertainty in the reserves. It will be important for the actuary to select the most appropriate approach given the circumstances. This will require the actuary to weigh up the costs versus benefits of the different approaches.
There are three commonly used approaches for quantifying uncertainty: 
stochastic models  
alternative sets of assumptions scenario testing.

Question 20

What are the 3 commonly used approaches for quantifying uncertainty in reserves?

Answer 20

There are three commonly used approaches for quantifying uncertainty: 
stochastic models  
alternative sets of assumptions scenario testing.

Question 21

Quantifying uncertainty in reserves:
Method 1 - Stochastic reserving

Answer 21

One way to quantify the uncertainty in a reserve estimate is to construct a stochastic model of the claim development process.

1. One model of particular interest is the so-called over dispersed Poisson (ODP) model.
   This is a generalised linear model (GLM) applied to claims triangles where the form is chosen so that the mean (or best estimate) reserve is equal to that resulting from a deterministic basic chain ladder method.
   We can obtain a distribution of possible outcomes from this model that reflects both parameter risk and process risk by using a bootstrapping technique. We have discussed this in Chapter 16 (in the section ‘Bootstrapping the ODP’)
2. Another model is the Mack model (previously discussed in Chapter 16). This calculates the mean and variance (including parameter uncertainty) of the distribution of possible outcomes. We choose a parametric distribution with this mean and variance, if we require a full distribution of possible outcomes. We typically choose a positively skewed distribution (for example, a log-normal or gamma distribution).
   Using these models, we attempt to quantify process and parameter error, but we may not obtain a reasonable answer. There are various reasons why any method might provide unreasonable results:
   
   The past data upon which these methods are based might be affected by one-off events, such as changes in claims handling procedures. As we do with a deterministic method, we need to adjust the parameters or results to allow for these features.
   
   The remaining volatility seen (after adjusting for changes within the claims environment), within the historical claims development may not be a good indicator of the underlying process uncertainty.
   This is particularly a problem for insurers or classes of business for which there are only a few years’ historical (and consistently derived) data. Often the assumptions inherent in these methods may not hold true in practice.
     
   We have limited data, which will not reflect even a small proportion of possible outcomes.
   The choice of model (in this case the chain ladder method) may not be a good representation of the underlying process (eg the chain ladder method may not be the best model to use to set reserves for war insurance).
   Although it is possible to allow for the more extreme correlations that may occur in the tail of distributions using a stochastic approach, eg by using Gumbel correlations; these are in practice very difficult to parameterise except by the use of judgement.
   The Gumbel copula is discussed elsewhere in the course.
   We should also remember that both the ODP and Mack methods are based on the chain ladder reserving technique. The variances which are derived are related to estimates from this method. Quite often an estimate has been derived from a different method, such as the Bornhuetter-Ferguson method. We should consider the extent that the estimation method may change the volatility estimate.
   A stochastic model will not always be appropriate. An approach taking into account the actuary’s knowledge and experience and more based on judgement can be more suitable.

Question 22

Key assumptions in a Bootstrapping the ODP model

Answer 22

The key assumptions used when bootstrapping the ODP are: 
  
the run-off pattern is the same for each origin period (as for the chain ladder) incremental claim amounts are stochastically independent
the variance of the individual claim amounts is proportional to the mean incremental claims are positive for all development periods.

Question 23

Quantifying uncertainty in reserves:
Method 2 - Alternative set of assumptions

Answer 23

Another way to quantify the uncertainty in a reserve estimate is to estimate the reserve using parameters different to those of the best estimate. The resulting spread of reserve estimates provides a range around the best estimate reserve. We usually determine the sets of assumptions using judgement.
We would often ‘flex’ our existing assumptions rather than determine an entirely different set of assumptions. For example, to determine a higher estimate, we may lag the claims development pattern by one quarter and assume our IELR estimates are understated by 5%.
You may intuitively want to call this a scenario analysis. In this context however, a scenario analysis refers to the method of testing extreme scenarios, rather than the more likely, less extreme outcomes discussed here.
We note that we should view each set of assumptions as a package so that each individual assumption may be correlated with others. In particular, inflation and discount assumptions are typically correlated.
The main advantages of this method are: 
 It is very simple to perform on deterministic or stochastic models.
We use judgement when we select possible parameters. We can therefore allow for atypical volatility in the historical data.
For example, if it is not expected to be repeated then it can be excluded from consideration.
This is a possible advantage over the stochastic models described above where parameter uncertainty is related to the volatility of the historical data.
The main disadvantages of this method are: 
 
We assign no explicit probability to each set of parameters. Therefore, it is not possible to estimate the distribution of future outcomes unless we assign a probability to each set of assumptions.
We ignore model uncertainty using this method.
We do not allow for process uncertainty if we use alternative sets of assumptions for a deterministic model. However, there is no reason why we cannot use alternative sets of assumptions for a stochastic model.

Question 24

Suggest what type of uncertainty we are allowing for if we use alternative sets of assumptions for a deterministic model.

Answer 24

Parameter uncertainty.

Question 25

Quantifying uncertainty in reserves:
Method 3 - Scenario testing

Answer 25

A third way to quantify the uncertainty in a reserve estimate is scenario testing. In a scenario analysis, we often examine the likely impact of catastrophic events on an insurer’s outstanding liabilities. In extreme conditions, many areas of uncertainty may become more correlated than in normal conditions. The interdependency of these uncertainties is a key aspect of any extreme scenario.
For example, in a scenario test, we might estimate the required reserves if a latent asbestos-type claim emerges, which affects several industries and insurance classes and causes some of the company’s reinsurers to default.
We normally use scenario analyses to investigate the top limit of the range of possible outcomes for the outstanding liability.
We can derive a scenario in a variety of ways: 
basing it on an historical event
 
thinking up a hypothetical event using our judgement or from the results of a stochastic model.
Scenarios are typically based on unlikely, but not impossible, events. These events can be financial, operational, legal or related to any other risk that might have an impact on the insurer’s outstanding liabilities. We can develop scenarios with varying complexity.

The aim is to make sure all sources of risk are identified and key risks are analysed in detail and quantified. It is useful to divide risks into appropriate categories for this purpose.
We may also wish to test the effects of plausible favourable scenarios to prepare responses to capitalise on such events if they should occur.

Question 26

A company writes employers’ liability business. Give an example of: (i)
a financial risk
(ii) an operational risk (iii) a legal risk that might have an impact on the company’s outstanding liabilities.

Answer 26

(i)
Financial risk – failure of a capital provider, failure of assets.
(ii) Operational risk – mismanagement of the portfolio, poor data recording and lax claims handling.
(iii) Legal risk – a court precedent increases the level of claims.

Question 27

Some typical scenarios affecting outstanding liabilities are used in scenario testing

Answer 27

Some typical scenarios affecting outstanding liabilities are: 
Single catastrophes.  
Major individual contracts written. We can check these in isolation, or check combinations of them. The test should analyse all risks included within these contracts.
Multiple ‘large’ losses. We can consider the possibility of random events or possible common causes (for example, economic downturn / problems with financial institutions) causing a series of losses. These might hit a significant part of syndicate retention (for a Lloyd’s syndicate) or potentially exhaust lower layers of reinsurance programmes.
      
Poor attritional claims experience. Latent claims.
Reinsurance bad debt.
Interest rate changes (if discounting reserves). Inflation levels.
Expense levels. Exchange rate movements.

Question 28

The main advantages of scenario testing are:

Answer 28

It provides an advantage over a stochastic model by allowing a more detailed analysis of the tail end of the reserve distribution.
A stochastic approach will produce a distribution of outcomes that will enable us to derive the percentiles of the distribution. The tail of this distribution of outcomes will generally occur when a number of adverse factors coincide. It is very difficult to model such a coincidence of factors reliably using a parametric approach. –
We should treat the results from stochastic modelling with a great deal of care when we consider the tails of the distribution.
– 
In performing a scenario test, we pay particular attention to the likely coincidence of these adverse factors.
A scenario analysis is more focused. Unlike a stochastic approach which provides a full analysis even when we may only be interested in the extreme outcomes.
Therefore, it is more time consuming and expensive to run. We can aim a scenario test at the specific question being asked.

Because it is aimed at the specific question, we can construct a scenario test and produce reliable results much more quickly than for a stochastic model. It can be used to help set the margin of an insurer as well as understand truly adverse scenarios.
It is easier to communicate the results of scenario tests than the results of stochastic models, as they are more transparent. The management of the business or users will typically understand the scenarios used, and can form an opinion of the tests without requiring detailed explanation. A stochastic model is rarely able to be challenged in a real-world scenario by management so limits the practical uses and the confidence they can have in the results.

Model uncertainty is much less of a problem when we construct scenario tests because we consider the driving factors explicitly. Stochastic models may fail to capture some features of the real life process, especially under extreme circumstances.

Question 29

The main disadvantages of scenario testing are:

Answer 29

The main disadvantages are: 
There is no specific probability associated with the outcomes and so it is not possible to construct a distribution of outcomes. But we could sometimes argue this is more appropriate than the possibly spurious accuracy in the tail of distributions that we calculate using a stochastic approach.

Scenarios typically only give information on the extremes of the distribution of eventual outcomes.
The actuary may want to disclose information on the overall distribution to stakeholders too.

The method is more subjective than the other two methods. This is because the actuary has to decide which extreme scenarios are to be investigated.

Question 30

For quantifying the uncertainty in reserves which of the 3 methods is likely to be used in practice?

Answer 30

In practice, we are likely to use all or a combination of the above techniques. 
This will be in part dependent upon the stability of the class of business and the credibility of the past data available. 
We should select the approaches which are appropriate to the scale, complexity and importance of the analysis, taking into account the cost / benefit balance to the user.

Question 31

Points to consider when communicating best estimate reserves

Answer 31

The commonly used phrases ‘best estimate’ or ‘central estimate’ can mean different things to different people.
Furthermore, we should not communicate the best estimate in such a way that gives the impression that it is the only ‘right’ answer or ‘point’ estimate. Rather, when providing a point estimate, it is important that the actuary is able to communicate effectively the inherent uncertainty surrounding that estimate to key stakeholders.
There is a range of possible outcomes because of the uncertainties described above. Some outcomes are more likely than others. We should make clear that the best estimate is the mean (or median) of the distribution of the range of possible outcomes. The best estimate does not necessarily represent the most likely outcome, especially if (as is usual) the distribution of the range of possible outcomes is positively skewed.
A positively skewed distribution will have a tail extending out to the right (larger numbers). For this distribution, the mean is greater than the median reflecting the fact that the mean is sensitive to each score in the distribution and is subject to large shifts when the sample is small and contains extreme scores.
The best estimate is just an estimate. There can be a tendency for the best estimate to be treated as being a more reliable prediction than it is intended to be and really is. Any user of the information should understand that it is just an estimate, that there are other possible reasonable estimates and that the ultimate result is almost certain to be different to the estimate.
We should also highlight the key assumptions made. There will often be a number of critical assumptions to which the best estimate and/or reserve ranges are most sensitive. The reliability of the result will depend on the appropriateness of these assumptions. The user needs to be aware of what these assumptions are and the sensitivity the result has to these.
TAS 100 states that communications shall state the material assumptions and describe their rationale.
We should comment on the main restrictions (or shortcomings) in the analysis. These could include incomplete data, restrictions in the scope of the work or lack of information provided on company policies.
For example, TAS 100 states that communications shall: 

include explanations of any significant limitations of the models used and the implications of those limitations
describe any material uncertainty in the data and the approach taken to deal with that uncertainty.
It may be that the actuary wants to present an overall measure of uncertainty for the company, eg by combining the results from the individual classes of business. In this case some adjustment may be made to the figures to reflect the benefits of diversification.

Question 32

Communicating uncertainty in reserves

Answer 32

For many purposes, it will be appropriate to give an estimate of the uncertainty surrounding the best estimate by giving a margin or range. A range of reserve estimates can help key stakeholders understand the uncertainty inherent in the business. In this case it will also be necessary to define the meaning of the margin or range and communicate it carefully.
For example, when selecting a reserving basis where we make key judgements that have a material impact on the estimates, we should communicate these key judgements when giving the estimates.
TAS 100 states that material judgements shall be communicated to users so that they are able to make informed decisions.
We should state clearly the extent to which the margin or range is intended to reflect the various sources of uncertainty.
The terms used to describe the sources of uncertainty can mean different things to different people. When describing a reserving basis, we should define these terms carefully and communicate them in a way that is appropriate to the audience.
The purpose for which the reserving exercise is being carried out has a direct effect on the importance of the uncertainty surrounding the reserving process and estimates. This in turn may affect the reserving basis selected for the purpose in question.
The Technical Actuarial Standard 100 requires that actuarial communications indicate the nature and extent of any material uncertainty in the actuarial information they contain.
Note: on the assumption that the phrase ‘best estimate’ means the actuary’s best view of the mean or expected value of the eventual outcome (possibly excluding certain remote contingencies), then we can think of a range described as ‘a range of reasonable best estimates’ as illustrating the parameter uncertainty and model error alone.
Since actuarial judgement is involved to a greater or lesser extent in all of the methods of quantifying uncertainty, different actuaries examining the same tranche of business would produce somewhat different illustrations of uncertainty.
In recent years, actuaries have increased their focus on communicating uncertainty. Misunderstandings can sometimes occur because our stakeholders, who may have less technical training in the details of uncertainty, are not as familiar with some of the concepts as actuaries. Actuaries need to be careful to communicate uncertainty in a way which is intuitively comprehensible to non-actuaries. Stakeholders have expressed a strong preference for being told the range of potential outcomes. This is an intuitively straightforward concept and is directly relevant when we track the actual out-turn (outcome) of claim costs.

The quantification of uncertainty requires us to communicate both size and likelihood of the reserving requirements. The size is normally quoted explicitly, whereas the likelihood is normally communicated in two ways.
We can communicate uncertainty in two ways: 1.
using words
2. using numbers (often expressed in percentiles). In practice, it is likely to be a combination of these two approaches.
The use of percentiles is a way of communicating uncertainty not a way of estimating the uncertainty. For example, the actuary may have exercised judgement to examine alternative sets of assumptions when estimating uncertainty but this can still be communicated using percentiles.
The method we choose depends on the technical knowledge of the audience, but we note that any valuations of percentiles may imply more certainty of the distribution than is warranted. It is worth stressing that a percentile is often a percentile within a particular model and is not immune to residual model error (or indeed parameter error).
An example of adopting the percentile approach when communicating to the audience would be to say:
‘… this equates to the 90th percentile, meaning that in my judgement there is a 90% chance that the outcome will lie below this value and a 10% chance that it will lie above.’

Question 33

List the four sources of uncertainty in a reserving model.

Answer 33

Specification error, selection error, estimation error and process error

Question 34

Without referring back to your notes, write down three types of ranges that might be used by actuaries.

Answer 34

Range of best estimates, range of possible outcomes and range of reasonable / probable / plausible outcomes.
You should ensure that you clarify which of these ranges you mean when communicating your results.

Question 35

3 Types of ranges that might be used

Answer 35

• range of best estimates
• range of possible outcomes:
  ‘Range of possible outcomes’: this would represent the actuary’s estimate of the complete range of outcomes for future claims. It would therefore be significantly wider than the range of best estimates and rarely of much practical use for live portfolios.
• range of reasonable / probable / plausible outcomes:
  this would typically be wider than a range of best estimates, but much narrower than the range of possible outcomes.
  It would be wider than a range of best estimates because it would allow for outcomes that cannot be reasonably regarded as an estimate of the mean or average outcome, but which can still be regarded as plausible outcomes.
  We can think of this range as allowing for parameter / model uncertainty and some element of process uncertainty as well. It would effectively include the outcomes that the actuary regards as plausible or probable but exclude those outcomes that the actuary regards as extreme (being either very low or very high). It would exclude the very extremes that would be included in a range of possible outcomes (in general this would not include the possibility that no further claims are paid).

Question 36

“Range of possible outcomes”

Answer 36

This would represent the actuary’s estimate of the complete range of outcomes for future claims.
It would be considerably wider than the range of best estimates.

There are three commonly used approaches for quantifying uncertainty:

1. stochastic models
2. alternative sets of assumptions
3. scenario testing.

Question 37

“Range of reasonable / probable / plausible outcomes”

Answer 37

This would typically be wider than a range of best estimates, but narrower than the range of possible outcomes,
… since it would allow for outcomes that cannot reasonably be regarded as an estimate of the mean or average outcome.

Question 38

2 Advantages of using the “Alternative sets of assumptions” method

Answer 38

• It is simple to perform on deterministic or stochastic models
• We use judgement when we select possible parameters. We can therefore allow for atypical volatility in the historical data.

Question 39

3 Disadvantages of using the “Alternative sets of assumptions” method

Answer 39

• We assign no explicit probability to each set of parameters.
• We ignore model uncertainty using this method
• We do not allow for process uncertainty if we use alternative sets of assumptions for a deterministic model.

Question 40

Scenario analysis

Answer 40

WHAT 1. In a scenario analysis, we often examine the likely impact of catastrophic events on an insurer’s outstanding liabilities.
WHY 2. In extreme conditions, many areas of uncertainty may become more correlated than in normal conditions. The interdependency of these uncertainties is a key aspect of any extreme scenario.

For example, in a scenario test, we might estimate the required reserves if a latent asbestos-type claim emerges, which affects several industries and insurance classes and causes some of the company’s reinsurers to default.

Scenarios are typically based on unlikely, but not impossible, events. These events can be financial, operational, legal or related to any other risk that might have an impact on the insurer’s outstanding liabilities. We can develop scenarios with varying complexity.

Question 41

Scenario analysis:
3 ways of deriving a scenario

Answer 41

• basing it on an historical event
• thinking up a hypothetical event using our judgement, or
• from the results of a stochastic model

Question 42

Scenario analysis:
10 Typical scenarios affecting outstanding liabilities

Answer 42

• claims outstanding from single catastrophes
• claims outstanding on major individual contracts
• multiple large losses
• poor attritional claims experience
• latent claims
• reinsurance bad debt
• interest rate changes (if discounting reserves)
• inflation levels affecting the ultimate size of claims paid
• expense levels
• exchange rate movements if claims are paid in foreign currency.

Question 43

6 Main advantages of scenario testing

Answer 43

• A scenario analysis is more focused.
• We can construct a scenario test and produce reliable results much more quickly than for a stochastic model (since it is aimed at the specific question)
• Provides an advantage over a stochastic model by allowing a more detailed analysis of the tail end of the reserve distribution.
• In performing a scenario test, we pay particular attention to the likely coincidence of these adverse factors.
• It is easier to communicate the results of scenario tests than the results of stochastic models, as they are more transparent.
• Model uncertainty is much less of a problem when we construct scenario tests because we consider the driving factors explicitly.

Question 44

3 Main disadvantages of scenario testing

Answer 44

• No specific probability associated with the outcomes and so it is not possible to construct a distribution of outcomes.
• Scenarios typically only give information on the extremes of the distribution of eventual outcomes, while the actuary may want to disclose information on the overall distribution to stakeholders too.
• The method is more subjective than the other methods, since the actuary makes the decisions on which extreme scenarios are to be investigated.

Question 45

Model error

Answer 45

Model error arises because actuarial models are often a simplification of a very complex (and unknown) underlying system. By using a simplified model to project the true underlying system, an unknown bias is introduced into the model. This results in uncertainty in the estimates produced by the model.
In addition to model error, there are two further sources of error, parameter (or estimation) error and process error.

Question 46

Estimation or parameter error

Answer 46

Arises from the fact that the estimated parameters are random variables.

Question 47

Selection error

Answer 47

Arises from incorrect selection of the underlying data used.

Question 48

Specification error

Answer 48

Arises from the specification of the model.