14 - Modelling Flashcards
What are the objectives of a model?
The primary objective in building a model is to enable the actuary advising an entity to give appropriate advice so that it can be run in a sound financial way. Models will therefore be used to assist in the day-to-day work done for the entity and to provide checks and controls on the business.
What factors influence the number of model points chosen?
- The availability and power of computers
- The variability of contracts sold
- The complexity of the contracts in force
- The age of the company
- Whether the model is stochastic or deterministic
- The purpose and importance of the investigation
- The time available
- The sensitivity of the results to using more or fewer model points
- The availability and credibility of the data
What are the requirements of a good model?
- The model being used must be valid, rigorous, and adequately documented.
- The model chosen should reflect adequately the risk profile of the classes of business or financial products being modelled.
- The parameters used must allow for all features of the business being modelled.
- The inputs to the parameter values should be appropriate to the business being modelled.
- The workings of the model should be easy to appreciate and communicate.
- The outputs from the model 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 should not be 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.
- A range of methods of implementation should be available to facilitate testing, parameterisation, and focus of results.
- The model should exhibit sensible joint behaviour of model variables.
- A model needs to allow for all the cashflows that may arise.
- A model needs to allow where appropriate, for the cashflows arising from any supervisory requirement to hold reserves and to maintain an adequate margin of solvency.
- A model needs to allow for the distinction between physical cashflows and notional cashflows.
- The model will need to project separately the cashflows arising from different states and reflect the transitions between these states.
- The cashflows need to allow for any interactions, particularly where the assets and the liabilities are being modelled together.
- The ability to use stochastic models and simulation needs to be allowed for.
List the general steps in a modelling process.
- Set out the objective of the model or the modelling process.
- Select an appropriate model structure, in other words which business areas or fund categories to include.
- Decide which variables, for example, claims costs, premium growth, to include, and define their inter-relationships.
- Determine the types of scenarios to develop and model, for example, interest rate environment, competitive environment.
- Collect the data needed and make any adjustments needed.
- Determine the model points to use in the model, making modifications to allow for any expected changes in business or mix in retirement states may change during the period.
- If a stochastic model is being used, choose a suitable density function for each of the variables to be modelled stochastically.
- Estimate the parameters that should be used for each variable, that is, the mathematics that specifies the behaviour of each variable.
- Ascribe values to the variables that are not being modelled stochastically.
- Construct and run the model.
- Aggregate output from various sub-models.
- Test and validate the reasonableness of the assumptions and their interactions.
- Check and analyse the model fit and significance of the variables in the model, which includes sense checking the results to ensure they make reasonable sense.
- Perform sensitivity testing on the model and its results.
- Extract and interpret the modelling results.
- Ensure that the model process has been well documented and has been checked.
- Summarise the model results and determine the appropriate conclusions.
What are the two main approaches to modelling for health and care and retirement benefits?
- Formula approach
- Cashflow approach
What are the key features of a stochastic approach?
- Some of the parameters in a stochastic model, for example, number of claims or claim amounts, are allowed to vary and have their own distribution functions.
- A stochastic model must be run many times using random samples from the distribution functions, often called ‘simulations’.
- The model produces results in the form of a probability distribution.
- The model is run using different distributions / parameters to check sensitivity.
What are the key features of deterministic models?
- Each of the parameters in a deterministic model has a fixed value.
- The model produces results in the form of a point estimate.
- It is possible to sensitivity test the results of a deterministic model by running the model with different parameter values.
In which examples a stochastic model would be invaluable?
- When trying to assess the impact of guarantees
- When the variable of interest does have a reasonably stable and predictable probability distribution, for example, investment returns in a developed economy under stable economic and political conditions
- For indicating the effect of year-on-year volatility, random fluctuations, on risk
- For identifying potentially high-risk future scenarios, for example, by tracing the sequence of events that have led to the worst simulated outcomes
What are the disadvantages of stochastic modelling relative to deterministic modelling?
- Time and computing constraints, mean that stochastic modelling work might be done with a very simplified version of the model.
- The sensitivity of the results to the deterministically chosen—assumed values of the parameter(s) involved, for example, If a normal distribution is assumed, then the mean and variance are the—deterministically chosen—parameters.
- Deterministic models are more readily understandable and explicable to a non-technical audience; the scenarios being modelled, and the model output are also clearer and easier to understand.
What are explanatory variables?
The selection of the explanatory variables to be included in the model will depend on the purpose of the model. In a pricing context, the explanatory variables would typically be rating factors.
What are response variables?
These are outputs from the model that are likely to be affected by the explanatory variables.
What are categorical variables?
These are explanatory variables that are used for modelling where the levels of each level are distinct, and often cannot be given any natural ordering or score.
What are non-categorical variables?
These are explanatory variables that take numerical values, for example, age.
What is an interaction term?
This is used where the pattern in the response variable is better modelled by including extra parameters for each combination of two of more factors.
What is a link function?
This acts to remove the assumption that the effects of different variables must simply be added together. Instead, it defines a more complex yet appropriate relationship between the explanatory and response variables.
What is a Generalised linear model (GLM)?
A GLM is a flexible generalisation of linear regression. GLMs model the behaviour of a random variable that is believed to depend on the values of several characteristics, for example, age, gender, and chronic condition.
What is multi-state modelling?
Multi-state modelling is used where policyholders can exist in different states, each state being associated with a different set of cashflows.
What is parsimony?
In general, parsimony applies that as few parameters as possible should be used to find a satisfactory fit to the data.
What are degrees of freedom?
The number of degrees of freedom (df) for a model is defined as the number of observations less the number of parameters.
What is deviance?
This compares the observed value to the fitted value, with allowance for the weights, and assigning higher importance to errors where the variance should be small. In essence, the deviance is a measure of how much the fitted values differ from the observations.
What is the Akaike Information Criterion (AIC)?
In cases where models are not nested, the AIC can be used to compare them. The AIC for a model is calculated as: AIC = -2 * log likelihood + 2 * number of parameters.
What is the Cramér-Rao lower bound (CRLB) theorem?
The Cramér-Rao lower bound (CRLB) theorem can be used to measure uncertainty in the estimators of model parameters in a generalised linear model (GLM). The standard error for a parameter estimator θ is the square root of the CRLB. A poorly defined parameter will have a large standard error. A higher CRLB gives a lower estimate for the variance of an unbiased estimator. If estimators are close to the CRLB, they are more unbiased.
What is a Hat matrix?
The hat matrix H gets its name from the fact that it shifts the vector of observed values to the vector of fitted values.
What is leverage?
The diagonal element of the hat matrix is called the leverage and always lies between 0 and 1. It can be viewed as a measure of how much influence the nth observation has over its own fitted value.
