Capital modelling methodologies Flashcards
(17 cards)
- Available capital
o The excess of an insurer’s financial assets over the value of liabilities is colloquially known as capital, and more specifically, available capital
o There are 2 types of required capital
The amount of capital an insurer is required to hold for regulatory purposes – known as regulatory or solvency capital
The amount of capital that a provider determines is appropriate to hold given its assets, liabilities, and business objectives, this is known as economic capital and will be higher than the minimum regulatory capital
Most insurers hold more capital than the minimum specified by their regulators
- To reduce the risk that the available capital falls below the regulatory requirement, which would hamper the firm’s business activities
- To give a greater degree of security to policyholders than implied by the relatively weak regulatory minimum
- To maintain its credit rating
- To meet the requirements of other stakeholders such as debt providers, whose interests may be subordinated to those of the policyholders
- To maintain a level of working capital for investment in business development and other opportunities
- To allow a buffer between the actual profitability of the business and the dividend stream paid to shareholders, who prefer less volatile returns
o Capital models can be characterised by three core features
A risk profile, which is defined by the risks being modelled and the key outcome being used to measure success or failure
A risk measure, which links the outcome to the capital required to achieve that outcome, it will be defined in terms of a required confidence level and a time horizon
A risk tolerance, which is the required level of confidence stated in the risk measure
o Insurance risk:
Insurance risk is defined as the risk of loss arising from the inherent uncertainties about the occurrence, amount and timing of insurance liabilities, expenses and premiums. It is normally divided between:
* Underwriting risk, relating to risks yet to be written/ earned
* Reserving risk, relating to risks already earned
Net insurance risk can be calculated by deducting reinsurance costs (and premiums) from gross insurance risk. When calculating aggregate insurance risk (across business classes), allowance should be made for correlations.
Insurance risk may also be affected by:
* The underwriting cycle
* Parameter error
* Multi-year policies
* Management actions
* Reinsurance terms in future years
o Market risk
Market risk is defined as the risk that, as a result of market movements, a firm may be exposed to fluctuations in investment markets affecting the value of assets and liabilities. Sources of market risk include movements in interest rates, exchange rates, equity prices and property prices.
The risk will be greater if the insurer does not follow a matched investment strategy.
Assets may be modelled individually, in groups of similar assets or by using a notional portfolio.
Market risk can be modelled by simple stress testing or by using an ESG.
o Credit risk
Credit risk refers to the risk of loss if another party fails to meet its financial obligations, or fails to meet them in a timely fashion. It is typically split into:
* Investment credit risk
* Counterparty credit risk – the most significant counterparty is the reinsurer(s)
In each case, it will be necessary to consider the probability of default for each counterparty and the size of the loss given that the default event occurs.
It will be necessary to consider the different levels of risk in different environments, eg recessions.
Stochastic models may be used to model credit risk, however stress tests will still be needed to check the model for reasonableness and to help calibrate the assumptions.
o Operational risk:
Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. Operational risks include risks relating to administration, compliance, impact of events, fraud, governance, strategy, technology and pension scheme provision.
Some operational risks will overlap with other categories of risk
Due to its uncertain and subjective nature, operational risk is difficult to model and requires a considerable amount of judgement.
o Group risk:
Group risk is defined as the risk a firm experiences from being part of a group as opposed to being a standalone entity. The size of the group risk will depend on the ownership structure of the firm and how it is funded by the parent. Capital may not be a good mitigant for group risk.
Group risks might include: reputational risks, concentrated credit risks and risks arising from centralised functions.
o Liquidity risk:
Liquidity risk the potential that a firm is unable to meet its obligations as they fall due as a consequence of having a timing mismatch between assets and liabilities.
In assessing liquidity, the insurer should consider all factors that affect the quantity of liquid assets available to meet the liabilities. These factors might need to be analysed in conjunction with other risks (eg insurance and market risks).
o Additionally there are some general modelling considerations, including
All parties involved should understand the whole process
The model developers should understand the business deeply
The objectives of the model relate to an increased understanding of risk and capital by management, and decisions including the impact on risk and capital.
There are a number of decisions that a capital model can inform.
There is much uncertainty in the modelling process. Thorough testing should be conducted to understand the extent of uncertainty and it should be communicated appropriately to those using the output of the model in decision making.
The principle of proportionality and practicability should be considered when deciding on the level of detail to model
A detailed audit trail should be kept of the whole process, with special care to document the process of selecting key assumptions and other key decisions.
o Methods of allocating capital:
Percentile method – can be applied to the output of a stochastic model, we would take the simulation which determines the capital requirement and assess how the loss in that simulation was made uo
Marginal capital method – here we allocate the capital with reference to the marginal capital requirements of each segment
Shapley method – we allocate the capital with reference to an average of the marginal capital requirements, assuming that the class under consideration is added to the overall portfolio first, second, third and so on
Proportions method – allocate economic capital to each class of business in proportion to its contribution to the risk metric on a standalone bases
o Features of a good model –
The model chosen should reflect adequately the risk profile of the classes of business being modelled
The 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 who advice will be given
The model should be sufficiently detailed to deal adequately with the key risk areas and capture homogeneous class 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, nothing complex can be successfully designed and built in a single attempt
o Additional features of a good stochastic model –
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
Be capable of being run with changed parameters for sensitivity testing
Use a large number of simulations
Have a robust software platform
Stochastic modelling
- Select an appropriate model structure
- Decide which variables to include, and their interrelationships
- Determine the types of scenarios to develop and model
- Collect, group and modify the data, ie information relating to the policies or members
- Choose a suitable density function for each of the variables to be modelled stochastically
- Estimate the parameters that should be used for each variable
- Test and validate the reasonableness of the assumptions and their interactions
- Ascribe values to the variables that are not being modelled stochastically
- Construct a model based on the chosen density function
Advantages of stochastic models
- Stochastic models test a wider range of scenarios, a scenario analysis under a deterministic approach can only test a limited set of scenarios
- We can derive a probability distribution from the outcomes of a stochastic model and calculate confidence levels, if required
- Even if we have calibrated individual stresses in a deterministic model to represent a certain degree of extremity in their individual values, it is very difficult to combine those stresses and be sure that the final result represents a sufficiently extreme combination of circumstances, a stochastic approach, explores all possible combinations of stresses and can rank these against the chose risk measure
Advantages of deterministic models
- The model is usually easier to design and quicker to run
- 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
- 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, we can often make the results more comprehensible to them
- It can also 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
- By developing deterministic stresses and scenarios and extending the scenario modelling to scenario planning and ‘what if’ analysis, we can help to link the capital model with the risk register, helping to integrate capital and risk management
- It is clearer what economic scenarios have been tested
- We commonly use stress and scenario tests for those risks that cannot easily be modelled quantitatively and where more subjective judgement is required
- 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 correlations
