Chapter 20: Capital Modelling Methodologies Flashcards
Aim of a capital model
Can be used to help the insurance company determine the LEVEL OF CAPITAL TO HOLD.The model will also enable the company to better understand their risks and inform business decisions.
Components of a capital model
- Future Written Premium income-
-project premium income separately for each LOB,
-split by source of business,
-set assumptions after consulting sales, u/w and senior management
-when including new business and renewals, allowance will need to be made for expected rates of premium growth (and profitability) in the light of the company’s business plan, the competitive position and the effect of the insurance cycle. - Future claims -
-for each LOB split claims into
a. Attritional, large, cat claims,
b. IBNR,
c. development of notified claims i.e. IBNER,
d. claims from period of unexpired risk on existing business,
e. claims from business written in the future
-Outstanding claims can be estimated using projection methods (eg the chain ladder method).
-These methods can also be used as the basis for estimating the claim outgo in future periods.
-As an example of how the elements of insurance risk might be treated, potential claims arising from catastrophes are usually analysed using the output from proprietary catastrophe modelling software, or by using scenario tests if capital modelling software output is not available. - Future expenses -
-commissions are normally a % of WP,
-rental. staffing cost, it is based on projected business growth,
-The expenses relating to handling the claims can be allowed for either explicitly or implicitly (ie with the corresponding claims).
-If the insurer stopped writing any more business, the expenses would just be in respect of the existing business. - Ceded Reinsurance -
Assumptions about ceded reinsurance will need to take into account:
-any existing outwards reinsurance arrangements
-any changes that could be made to those arrangements
-planned new arrangements to cover unexpired exposures or business planned to be written
-any forecast changes in underlying direct exposures
-any expected softening or hardening of future reinsurance costs.
-Allowance should be made for recovery delays and defaults.
-Alternatively, claims could be projected net of recoveries, with a margin to allow for defaults and an adjustment to the development profiles to allow for recovery delays. - Investment returns - Assumptions about future investment return will depend on:
-the current investment portfolio held
-investment prospects and expectations around the future economic environment
-the current and projected future investment policy
-expectations on premium and claims payment patterns, which impact the run-off of reserves and investment assets.
-For all types of investment, it is important to make allowance for:
the expenses of investment,
the future volatility of capital values and investment income. - Environment -
Economic - A capital model will need to make assumptions about future inflation and future interest rates. These assumptions should be consistent with each other. Allowance may also be made for other features of the economy, for example, the increased moral hazard associated with increased claim frequencies during times of recession.
The insurance cycle - The model should also take account of the insurance cycle, as should any business plan underlying the model. In particular, it will need to allow for the fact that different classes of business may be at different stages in the cycle.
Operating environment - The model should also take account of what is happening internally within the company and its potential influence on future cashflows. For example the potential impact of high staff turnover on the ability to meet regulatory deadlines or the loss of an underwriting team on the ability to meet a business plan.
There should also be some consideration of potential changes in legislation and their impact, for example the potential impact of a change in the Ogden discount rate on future claims payments. - Risk measure - A capital model requires a defined risk measure, on which it will be calibrated. This includes the type and confidence, for example, a 99.5% VaR.
Explain why we might split premium income by source of business for future written premium income component of a capital model
The premium income from each source of business should be considered separately in order to allow correctly for delays and acquisition costs.
The allowance for the cost of running the business once an office has closed should be much more than the normal allowance for claims handling costs. Suggest why this might be the case. (After all, both approaches relate to the cost of settling the existing business…)
As the business runs off, fewer claims will be settled (incurring lower claims handling expenses), so the firm’s fixed expenses will become a larger and larger proportion of overall expenses.Usually, a firm would use new premium income to meet its fixed expenses, but in the case of a run-off business, extra capital must be set aside to finance this.
Suggest under what circumstances it would be acceptable to treat all the equity holdings as providing an infinite stream of dividends
Treating equities purely as an income stream assumes that none of the equity portfolio is ever realised. This might be the case if the value of the portfolio was less than the free reserves (ie equities are backing the free reserves not the technical reserves), and the liability outgo would be entirely covered either by income from assets (including equities) or the redemption proceeds from other assets (eg index linked securities). This means that the equities would never need to be realised to meet future liability outgo.
Explain what is meant by a 99.5% VaR.
Value at Risk (VaR) generalises the likelihood of underperforming by providing a statistical measure of downside risk. VaR assesses the potential losses on a portfolio over a given future time period with a given confidence level.Consider, for example, a VaR of £10m over the next year with a 99.5% confidence interval. This means that there is only a 0.5% expected probability of the underperformance (relative to a benchmark) being greater than £10m over the next year
The Value at Risk (VaR) is the loss at a predefined confidence level (eg 99.5%), specified over a particular time horizon. Consequently, if an insurer holds capital equal to the VaR, it will remain solvent over a particular time horizon with a probability of the confidence level (eg 99.5%) and be insolvent with probability of one minus the confidence level (eg 0.5%).The use of probabilities and confidence levels in the risk measure seems to imply that we need to use a stochastic model. However, VaR can be used as a risk measure for deterministic models too, but the decision as to what constitutes a 99.5% probability will be very subjective.
Stochastic model
One in which we assume some of the variables in the business plan have an underlying probability distribution.
This enables us to describe critical assumptions, and their financial implications, in terms of ranges of possible outcomes.
A stochastic model can be very complex and its results difficult to interpret.
It is worth remembering that the output from a stochastic model is only as useful as the underlying data input allows. As such, we should start the model process by gaining a thorough knowledge of the underlying data. Similar data issues apply equally to deterministic processes.
9 steps in building a stochastic model
- specify the purpose of the investigation
- set the risk measure eg. VaR
- select an appropriate model structure
- decide which variables to include, and their interrelationships.
- determine the types of scenarios to develop and model. eg. interest rates, competitive environment, etc.
- collect group and modify the data,
- choose a suitable density function for each of the stochastic variables
- estimate the parameters that should be used for each variable.
- test and validate the reasonableness of the assumptions and their interactions. If the goodness of fit is not acceptable, then attempt to fit a different density function(s).
- ascribe values to the deterministic variables
- construct a model based on the chosen density functions.
Running a stochastic model (3)
Once the model has been built,
- run the model many times, each time using a random sample from the chosen density function(s). The constructed model then calculates the net profit based on the values simulated from each pdf in the model.
- produce a summary of results that shows the distribution of the modelled results after many simulations have been run.
- run the model using different distributions / parameters to check sensitivity.
3 Advantages of stochastic model
- test a WIDER RANGE OF SCENARIOS
- we can derive a PROBABILITY DISTRIBUTION OF OUTCOMES
- A stochastic approach explores all possible combination of stresses and can rank these against the chosen risk measure.
9 Advantages of deterministic models
Exam style question - April 2015, Q3
A general insurance company is considering building a computer model to determine its capital requirements. Outline the advantages of building and using a deterministic rather than a stochastic model. [8]
- the model is usually easier to design and quicker to run
- we can introduce more detail and ensure use an intelligent selection of scenarios
- we can often make the results more comprehensible (understandable)
- Deterministic models are more readily explicable to a non-technical audience
- By developing stresses and scenarios we can help link the capital model with the risk register, helping to integrate capital and risk management
- It is clearer which economic scenarios have been tested.
- It is important to consider potential cause and effect relationship between risks.
- Even where we have used a stochastic model, stress tests using a deterministic model are useful to check / validate the model for reasonableness and to calibrate assumptions.
____________________________________________
It is important to consider potential cause-and -effect relationships between risks.
We may model such relationships better using deterministic relationships rather than relying on statistical dependence structures.
It is more straightforward and, therefore, quicker and cheaper to build a deterministic model than a stochastic one.
Deterministic model is easier to sense check…
and easier to flex.
It does not require the same level of expert resource as a stochastic model..
and gives rise to less risk of model error. There is less danger of parameter error…
and less danger of spurious accuracy, particularly in the tail.
A deterministic approach may be appropriate where there is less data.
By reducing the computational power necessary to generate many thousands of simulations, we can introduce more detail in other dimensions, such as detailed descriptions of reinsurance programmes or treatment of underlying risks.
This may aid the intelligent selection of a limited number of scenarios.
It could be more efficient than a stochastic model where we hope that the important scenarios appear amongst a larger number of randomly generated outcomes.
We can integrate the capital model more closely with risk management, by extending the scenario modelling to scenario planning and “what-if” analysis.
We commonly use stress and scenario tests for those risks that cannot easily be modelled quantitatively and where more subjective judgment is required.
This allows us to concentrate more on the more important areas of the distribution of outcomes for the key risks when a full specification of the distributions is impossible.
By developing deterministic stresses and scenarios, we can help to link the capital model with the risk register, helping to integrate capital and risk management.
It can be easier to communicate the results of stress and scenario tests to senior management, and to give them comfort as to the reasonableness of the overall capital value.
It is important that users of the output understand the results from the model as well as methods and assumptions.
By showing the effect of a limited range of stresses and scenarios – some of which may have been developed in consultation with those users – we can often make the results more comprehensible to them.
5 Features of a good model
Mnemonic - VAN FUR UP CAVE
- model should be valid, complete and adequately documented
- adequately reflects the risk profile of the classes of business being modelled.
- parameter values used should be appropriate for the classes of business, and investments being modelled.
- The outputs from the model and the degree of uncertainty surrounding them should be capable of independent verification for reasonableness and should be readily communicable to whom advice will be given.
- The model should be sufficiently detailed to deal adequately with the key risk areas and capture homogeneous classes of business, but not excessively complex so that the results become difficult to interpret and communicate or the model becomes too long or expensive to run.
- The model should be sufficiently flexible. The model should be capable of development and refinement
- In addition, a range of methods of implementation should be available to facilitate testing, parameterisation and focus of results.
- have all parameters clearly identified and justified
- be structured and documented so that it can be understood by senior management and board members who do not have actuarial expertise.
VAN FUR UP CAVE:
Valid
Adequately documented
Not overly complex
Flexible
Understandable by managers
Reflect risk profile
Uncertainty should be verifiable
Parameters identified and justified
Complete
Appropriate parameters
Verifiable
Easy to communicate results
5 Additional features of a good STOCHASTIC model
A good stochastic model should:
- be rigorous i.e. strictly applying to constraints and principles and self-consistent
- be capable of being run with changed parameters for sensitivity testing.
- use a large number of simulations to avoid simulation error
- have a robust software platform.
Deterministic models
A deterministic approach is one in which we assign fixed values to the variables or parameters (interest rate, inflation rates, claims rates and so on). Under a deterministic approach, we produce a single run for each set of fixed values. The standard formula under the Solvency II regime is an example of a deterministic model.
Explain what the main difference is between stress and scenario tests
Explain what the main difference is between stress+scenario tests and sensitivity analysis
In a stress test, a single parameter is varied. Stress tests therefore analyse the impact of individual risks in isolation. In a scenario test, a combination of parameters is varied. Scenario tests therefore analyse the combined impact of a number of risks.
So stress testing and scenario testing are used to gain an insight into the uncertainty of our results.
Sensitivity testing is used to gain an insight into which parameters have the greatest effect on the model result.
Steps in running a deterministic model
A deterministic model involves the following steps:
- specify the purpose of the investigation
- set the risk measure, eg Value at Risk (VaR)
-collect data, group and modify data
By data, we mean information relating to the policies (ie the mix of business and claims history) being modelled. It may be too time consuming to run each individual policyholder through the model. Therefore it is common to group together policyholders with similar characteristics into ‘model points’.
-choose the form of the model, identifying its parameters and variables
Parameters are any factors which would affect the decisions we make as a result of running the model. For example, if investment returns influence the premium charged then investment return is a parameter. Variables are the factors we are trying to test when running the model. For example, if we are setting the premiums for a product, then the premium is the variable.
-ascribe values to the parameters using past experience and appropriate estimation techniques, taking into account the risk measure being used and any correlations between parameters
The value assigned to any parameter is usually referred to as the assumption for that parameter. The full set of assumptions is referred to as the basis of our model.
- construct a model based on the expected cashflows
- check that the goodness of fit is acceptable and, if not, attempt to fit a different model
This can be done by running a past year and comparing the model with the actual results. run the model using the selected variables run the model using different parameters to check sensitivity. The model may also be run under different scenarios, ie testing the robustness of the results to many parameters changing at the same time, rather than changing single parameters in isolation
Choosing a suitable density function for claim severity when using a stochastic model
-One way to choose a suitable distribution for claim severity would be to plot each of the observed claims in a bar chart (or equivalent), by size of claim:
-Now convert the left-hand scale so that the total area under the curve is 1, ie by dividing through by the total number of observed claims.
-Then select a function, y = f(x) which has a similar shape to our plotted data. This is the probability density function (PDF).
The following loss distributions are often used:
-Frequency: Poisson, negative binomial
-Severity: log-normal, Weibull, Pareto.
-We would then select a method of fitting to find parameter values for our chosen distribution. eg method of moments or method of maximum likelihood and then select the one that gives the best fit to our data.
-The method and parameters that have been fitted would be scrutinised using a number of statistical tests to determine how well the observed claims fit the modelled claims.
-Particular attention must be paid to the ‘important’ part of the distribution. For example, some classes of insurance have very skew claim amount distributions. Care should be taken that the fitted distribution has a sufficiently long tail.
-In these cases, a distribution such as the Pareto which has a relatively long, thick tail should be used. With excess of loss reinsurance care should be taken to ensure there is a good fit close to the excess point.
-If the goodness of fit of the model is not adequate, the distribution or the parameters should be altered until the fit is good enough
Give an example of a financial guarantee that might arise in general insurance
A motor policy, which promises to refund the first year’s premium if the policyholder makes no claims in a five-year period.
Advantages of deterministic models
There are a number of benefits of a deterministic approach:
- The model is usually easier to design and quicker to run.
- It is important to consider potential cause and effect relationships between risks.
- We may model such relationships better using deterministic relationships rather than relying on statistical dependence structures.
- It is more straightforward and, therefore, quicker to build a deterministic model than a stochastic one.
- By reducing the computational power necessary to generate many thousands of simulations, we can introduce more detail in other dimensions, such as detailed descriptions of reinsurance programmes or treatment of underlying risks.
- This may aid the intelligent selection of a limited number of scenarios.
- It could be more efficient than a stochastic model where we hope that the important scenarios appear amongst a larger number of randomly generated outcomes.
- We can integrate the capital model more closely with risk management, by extending the scenario modelling to scenario planning and ‘what-if’ analysis.
- It is clearer what economic scenarios have been tested. As discussed above, the disadvantage of this point is that it requires thought as to the range of economic scenarios that should be tested. Since only a limited number of economic scenarios will be tested, there is a danger that certain scenarios, which could be particularly detrimental to the company, are not identified.
- We commonly use stress and scenario tests for those risks that cannot easily be modelled quantitatively and where more subjective judgment is required. This allows us to concentrate more on the important areas of the distribution of outcomes for the key risks when a full specification of the distributions is subject to substantial potential error.
- By developing deterministic stresses and scenarios, we can help to link the capital model with the risk register, helping to integrate capital and risk management (this would also apply in a stochastic environment by considering each individual simulation as a scenario).
- It can be easier to communicate the results of stress and scenario tests to senior management, and to give them comfort as to the reasonableness of the overall capital value.
- A deterministic model is more readily explicable to a non-technical audience (eg users of results of the model and senior management), since the concept of variables as probability distributions is not easy to understand.
- It is important that users of the output understand the results from the model. By showing the effect of a limited range of stresses and scenarios – some of which may have been developed in consultation with those users – we can often make the results more comprehensible to them.
- Deterministic models are good for checking / validating results of a stochastic model.
- Deterministic model stress tests can be used in conjunction with the results generated from a stochastic model. This provides additional context to the stochastic results as well as providing either independent validation or appropriate challenge.
Combining deterministic and stochastic approaches
In many cases a problem can be solved by a combination of stochastic and deterministic modelling. Variables whose performance is unknown and where the risk associated with them is high might be modelled stochastically, while other variables can sensibly be modelled deterministically. For these reasons, the stochastic approach is often limited to the economic assumptions, with demographic assumptions being modelled deterministically. It may be appropriate to use a blend of approaches:
-stochastic models for some risk categories
-stress and scenario tests for other risk categories
-ad-hoc methods for yet other categories.
In fact, there are various ways in which stochastic and deterministic approaches can be combined in a single model. For example, when modelling claim frequency and average claim size separately, we could:
-Determine the number of claims stochastically and associate this with a deterministic mean claim cost. Ideally the claim numbers would be divided into various homogeneous groups in terms of claim size.
-Determine the claim amounts stochastically for the (deterministically chosen) expected number of claims.
-Determine both claim amounts and numbers stochastically, using a collective risk model.
3 Key objectives of any capital requirement regime
To ensure that:
Senior management focus on risk management - a risk management framework should be central to this process.
There is a link between risk and capital setting - in making an assessment of capital adequacy, a firm should:- identify the significant risks facing the business- assess their impact (both prior to and post having controls in place)- quantify how much capital is required
The capital model is being used within the decision making process - we demonstrate this through clear documentation of all prudential risks, processes and controls.
The overarching objective is PH protection and for ensuring solvency of insurers
two broad approaches available to firms when producing a capital model,
- stress and scenario tests
- Stress tests consider different factors in isolation. Scenario tests consider several factors at a time.
- This approach is a deterministic approach, where the user chooses which stresses and scenarios to test. - economic capital models (also known as stochastic models or dynamic financial analysis (DFA) models).
- An economic capital model is a more integrated, holistic approach.
- It systematically models the effects of many interrelated risk factors using simulation techniques.
- Although these are significantly different in application, they are not in principle different, as a stochastic model is based on stress and scenarios weighted by probabilities.
- In a DFA model, stress tests are generated automatically and often cannot be ‘seen’.