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Marshall: A framework for assessing risk margins (Proposed framework for…
Marshall
: A framework for assessing risk margins
introduction
Current approach to assessing risk margins
Coefficients of variation (CoVs)
are determined for individual valuation portfolios or groupings of portfolios, where these groupings are made up with homogeneous risks
A correlation matrix
is populated with correlation coefficients reflecting the expected correlations between valuation portfolios or groupings of portfolios
Usually the key risks that are considered to cause portfolios to be correlated are considered in turn and the correlation between classes is categorised as high, medium or low with each category having associated correlation coefficient values
It is more the exception than the norm to include a quantitative analysis of past experience in the assessment of correlation effects. The main reason for this is that most quantitative techniques require a significant amount of data, time and cost to produce results that are sufficiently good
CoVs and correlation matrices are determined separately for claim liabilities and premium liabilities and further assumptions made about the correlation between these two components of the insurance liabilities
A statistical distribution is selected and combined with the adopted CoVs and correlation coefficients to determine the aggregate risk margin
The most common distribution adopted is the lognormal distribution
Practical framework for assessing risk margins
A number of key stakeholders have expressed some concern that the wide range of approaches adopted in practice to assess risk margins might lead to significant inconsistencies in the final outcomes
Structure of framework
Claims portofolio
Valuation class 1, usualy alines with lines of business
Homogenous claim 2
Independent risk
(random component of parameter and process uncertainty)
Systemic risk
(potentially in common across claim groups or valuation classes)
Internal to actuarial process
(parameter and model uncertainty)
External to the actuarial process
(process uncertainty)*
Homogenous claim 1
Valuation class2
Proposed framework for assesing risk margin
Souces of uncertainty
Systemic risk
Internal systemic risk
because the used approach is an imperfect representation of a real life process
External systemic risk:
The randomness of the insurance process ,It arises due to external changes in environment having an impact on insurance liabilities/models.
Independant risk
Parameter risk
, because the randomness of the insurance process makes it hard to select appropriate parameters for the models
Process risk
Pure effect of the randomness associated with the insurance process
The nature of quantitative modeling techniques
They are best suited to analysing sources of independent risk and past episodes of external systemic risk. for systemic risk, the analysis needs to be supplemented
1. Claims portfolio preparation
An important consideration is whether the valuation portfolio split adopted to determine central estimates of insurance liabilities
It may not be possible to conduct quantitative analysis at the same granular level as used for central estimate valuation purposes. The central estimate valuation portfolios may be too small for credible analysis or the valuation portfolio may be at a more granular level than makes sense
Consideration should be given to whether any valuation classes would benefit from a further allocation
2. Independent risk analysis
Approaches to analysis independent sources of risk
Mack method,
Bootstrapping
Stochastic chain ladder
GLM techniques
Bayesian techniques
Reasons stochastic modelling techniques do not enable a complete analysis of all sources of uncertainty
A good stochastic model will fit the past data well and in doing so it fits away most past systemic risk external to the valuation process, leaving behind largely random sources of uncertainty
Where it has not been possible to fit away all past systemic episodes of risk , the outcome of the analysis may be substantially affected by these episodes. Consideration then needs to be given to whether past episodes of systemic risk are reasonably representative of what one can expect in the future.
Even where one is comfortable that a model adequately reflects the volatility expected in the future , the model is highly unlikely to incorporate uncertainty arising from sources of internal systemic risk.
Main sources
Process risk (randomness)
parameter risk
3. Internal systemic risk analysis
Main sources of internal systemic risk
Specification error
: The error that can arise from an inability to build a model that is fully representative of the insurance process. Also, the information available may be such that the underlying process cannot be fully understood and the model structure is simplified as a consequence
Parameter selection error
: The error that can arise because the model is unable to adequately measure all predictors of claim cost outcomes or trends in these predictors.
Data error:
The error that can arise due to poor data or unavailability of data . Data error also relates to inadequate knowledge of the portfolio being analysed.
4. External systemic risk analysis
Main sources of external systemic risks
Economic and social risks
(EX: inflation)
legislative, Political and claim inflation risks
Likely to dominate the volatility of the claim and premium liabilities for long-tail portfolios
(EX: WC)
Claim management process change risk
The key here is to work closely with claim managers to understand the claim management philosophy and the process
(EX: change in claim reporting )
Expense risk
The uncertainty associated with the cost of managing the run off of the insurance liabilities or the cost of maintaining the unexpired risk until the date of loss
Event risk
Likely to dominate the volatility of the premium liabilities for property classes
(EX: property damages)
Latent claim risk
The uncertainty associated with claims that may arise from a particular source that is currently not considered to be covered
(EX:casualty claims )
Recovery risk
Consideration
Communicatin with business experts to indentify key risks and to quantify them
In the selection of the assumptions , the consolidation of the analysis issubstentially simplified if one can assume that each of the risk categories is independent. Certain risk categories may have to be combined to ensure that this assumption is valid
5. Analysis of correlation effects on each source of uncertainty
Difficulties of using quantitative methods to assess correlation effects
Available techniques are complex, require a lot of data. and ar time consuming.
These techniques will yield correlations that are heavily influenced by the correlations experienced in past data
It is difficult to separate the past correlation effects between independent and systemic risk
Internal systemic risk cannot be modelled using standard correlation modelling techniques
Even if modelling of correlation effects were practical, they are unlikely to yield results that could be aligned to the outcomes of the framework
Independent risks
Are uncorrelated with other sources of uncertainty
Internal systemic risk
Can be assumed to be uncorrelated with independent risk, and with each potential external systemic source of risk
The same actuary effect and the use of template or valuation models across different valuation are key considerations
The Link between the premium liability methodology and outcomes from the outstanding claim valuation are key considerations
External systemic risk
Correlation effects will arise from correlations between classes or between claim and premium liabilities from similar risk categories
External systemic risk categories may be partially correlated either within or between valuation classes. If so, the correlated risk categories may be aggregated into broader categories that are not correlated with other risk categories
For practical purposes, the correlation relationship between any two sources of uncertainty or risk categories can be considered to belong to one of a finite number of assumed correlation bands
The text uses five:
Nil: 0%/ Low: 25%/ Medium: 50%/ High: 75%/ Full: 100%
A hierarchical structure can be constructed for each systemic risk category containing correlations between the following components
Premium liabilities and outstanding claim liabilities for a class
claim liabilities for individual valuation classes and the relevant class of business dummy variables
Class of business dummy variables and root dummy variables
6. Consolidation of analysis into risk margin calculation
CoVs for each valuation portfolio, separately for outstanding claim and premium liabilities. In respect of independent risk, internal systemic risk and each potential external systemic risk category
Correlation coefficients between each source of uncertainty, risk category, valuation portfolio and outstanding claim/premium liability combination
For practical purposes, it is recommended that a simple linear correlation dependency structure be adopted to allow for the various correlation effects
When creating any correlation matrix it is important to include a check that the matrix is positive and symmetric
7. Additional analisis
Sensitivity testing:
Valuable insights into the sensitivity of the key assumptions can be gained by making them vary
Scenario testing:
It is often insightful to tie the risk margin outcomes back to a set of valuation outcomes by strengthening some of the key assumptions adopted for central estimate purposes to align the outstanding claim liabilities and premium liabilities with the provisions assessed including risk margins
Internal Benchmarking
: For each source of uncertainty, the adopted CoVs should be compared between valuation classes, for outstanding claim liabilities, premium liabilities and insurance liabilities
For
independent risk
, there are two main dimensions that should be considered in the context of internal benchmarking: portfolio size and length of claim runoff. The larger the portfolio, the smaller the CoV. The longer the claim runoff, the higher the CoV
For systemic risks
Claim liability CoVs for short-tail portfolios are likely to be lower than for similar long-tail portfolios
Premium liability CoVs for long-tail portfolios would normally be higher than outstanding claim liability CoVs for the same portfolios. Because the outstanding claim liability is built up for many years, the amount over time varies less than the premium liability.
Premium liability CoVs for short-tail portfolios would normally be lower than outstanding claim liability CoVs for the same portfolios. The outstanding claim liability will be smaller and more variable since there is no build-up over the years.
External benchmarking:
Can be beneficial when there is little information available for analysis purposes. More generally, the use of benchmarking should be as a sanity check
Hindsight analysis:
Involves comparing past estimates of claim liabilities and premium liabilities against the latest view of the equivalent liabilities
Is particularly useful for short-tail valuations where there is little serial correlation between consecutive valuations.
Mechanical hindsight analysis:
A mechanical approach to estimating the outstanding claims and premium liabilities by systematically removing the most recent claims experience
Independent risk, by focusing the analysis on periods where there was a degree of stability in the experience with few or no systemic trends
Internal systemic risk, by applying it using a range of actuarial methods and observing the differences in volatility outcomes
All past sources of uncertainty, by applying the approach across all past periods
Examples
Apply a chain ladder method on a triangle of claims data
Select ‘current’ development factors using an objective approach
Remove a diagonal of data one at a time and calculate development factors using the same objective method as above
Compare the change in development factors
8. Documentation and regulation
A full application of the framework should be conducted every 3 years
The key assumptions should be examined in the context of
Any emerging trends
Emerging systemic risks
Changes to valuation methodologies
Independent risk assessment
For premium liabilities
Consideration should be given to aligning the methodology adopted to analyse uncertainty with that used for central estimate purposes
Bootstrapping techniques offer less flexibility than GLM techniques but can be adapted to help in the assessment of random effects
For claims liabilities
The process of identifying past systemic episodes can only be enhanced if an actuary has a strong understanding of the possible systemic sources of risk for a particular portfolio
approches to estimate the risk
Mack
Boostraping
Stochastic CL
GLM
Bayesian techniques
Systemic risk assessment
Scorecard summary
1.
For each of the specification, parameter and data risk components, conduct a qualitative assessment considering a range of risk indicators and scoring these on a scale of 1 to 5. If more than one variable per componant, take the average
Examples of risk indicators
Specification error:
Number of models used and range of results, reasonableness checks conducted, subjective adjustments required, extent of monitoring and review
Parameter selection error:
Ability to identify and use predictors
Data error:
Extent, timeliness and reliability of information from business; access to data; quality of reconciliations of past data; extent of revisions to past data
2.
Apply weights to each risk indicator, reflecting its relative importance to the overall modelling infrastructure, and calculate a weighted average score
3.
Calibrate the weighted average score derived to a CoV in respect of internal systemic risk. The development of appropriate CoVs will likely involve a substantial amount of judgment.
Other information
Standard triangulation methods
will normally analyse predictors that have been aggregated to a reasonably high level or lag rather than lead the underlying drivers of the insurance process
Each of the risk indicators may be considered for both the outstanding claim and premium liabilities. Additional indicators may be considered for premium liabilities, for example, whether the outstanding claim liabilities are used as an input to the premium liability assessment
If more than one methodology has been deployed in the past, then a hindsight of the actual past performance of each method can be used to assess the relative performance of each method
It has been decided that the minimum CoV associated with a perfect model is unlikely to be much less than 5%
The CoV scale with respect to the scorecard scores is not linear, reflecting the view that the marginal improvement in outcomes between fair and good modelling infrastructures is less than the marginal improvement between poor and fair modelling infrastructures