Chapter 14 (Part 1) Flashcards
Q&A 14.7
Explain why stochastic modelling might be useful for healthcare insurance purposes. [5]
With health products, the future incidence experience is very difficult to predict.✓✓
The particular difficulty lies in the potential benefit amount✓, which may vary, e.g. by:
* Policy-specified inflation (LTCI) ✓✓
* Medical inflation (PMI)✓✓
* Changes in accepted medical protocols (PMI).✓✓
With such uncertainty✓ and hence volatility of cashflows✓, it is important to be able to project the distribution of possible future outcomes✓, and this is what stochastic modelling enables us to do✓.
It achieves this by:
Allowing some of the variables in the model✓ (e.g. number of claims or claim amounts)✓ to vary✓ and have their own probability distribution✓.
Simulating random drawings from the probability distribution many times, and hence producing simulated random outcomes from the model.✓✓
The set of simulated outcomes from the model can then be used to form an estimate of the probability distribution of the outcome.✓✓
Stochastic models and simulation also enable us, where appropriate, to assess the impact of financial guarantees.✓✓
Q&A 14.7
State any disadvantages that stochastic modelling may have compared to the use of deterministic models. [2]
- There may be time and computing constraints✓✓, so stochastic modelling work might have to be done with a very simplified version of the model✓.
- The outputs from the model are sometimes very sensitive to the (deterministically chosen!) assumed values of the parameter(s) involved.✓✓
- We may have little confidence about the probability distribution (and its parameters) chosen for the stochastic variables.✓✓
- The preceding two points can therefore lead to spurious accuracy✓, and hence render the results of the modelling of very little practical use✓.
Q&A 14.10
Discuss the principal requirements that should be met by an actuarial model used to assist in the financial management of a healthcare insurance company.
[6]
The model must be valid✓ and sufficiently rigorous✓ for the purposes✓ to which it will be put, and adequately documented✓.
However, some approximations may be made for reasons of practicality.✓✓
The model points✓ chosen must adequately reflect the distribution of the business✓ being modelled. This may or may not include model points for new business.✓
The components of the model✓ must allow for all those features of the business✓ being modelled that could affect the advice being given✓. Examples of such parameters include inflation, withdrawals, and morbidity experience.✓✓ The parameters must be set appropriately, taking account of the features✓ of the company, and the business environment✓ in which it operates.
The model should exhibit sensible joint behaviour✓ of model variables, e.g. the assumed rate of investment return should be consistent with the assumed rate of inflation.✓✓
The workings of the model should be easy to appreciate and communicate.✓✓
The results should be displayed clearly.✓✓
The outputs✓ from the model should be capable of independent verification✓ for reasonableness✓. The output should also be readily communicable to those to whom advice will be given.✓✓ This will include the output being in a suitable format.✓ The model should not be so complex✓ that the results become difficult to interpret✓, …
… or the model takes too long✓ or costs too much to run✓, unless this is required by the purpose of the model✓.
Any shortcomings of the model should be clearly stated.✓✓
The model should be capable of subsequent development and refinement.✓✓
Question 14.9
A proprietary healthcare insurance company issues a wide range of conventional and unit-linked products.
State the requirements that should be met by an actuarial model, which will be used for calculating the value of the profits from the company’s existing business. [5]
The model must be valid✓ and sufficiently rigorous✓ for the purposes✓ to which it will be put, and adequately documented✓.
The model points✓ chosen must be such as to reflect adequately the distribution✓ of the business being modelled.
Alternatively, the company’s actual policy data file✓✓ could be used, provided the software was able to handle the computations effectively.
The components✓ of the model must allow for all those features in the business✓ being modelled that could significantly affect the advice being given✓.
The parameter values✓ chosen should be appropriate to the business being modelled✓ …
… and take account of the special features✓ of the company and the economic and business environment in which it is operating✓.
The model should exhibit sensible joint behaviour of model variables.✓✓
The workings of the model should be easy to appreciate & communicate.✓✓
The results should be clearly displayed.✓✓
The outputs from the model✓ should be capable of independent verification✓ for reasonableness
… and should be readily communicable✓ to those to whom advice will be given✓.
The model should not be overly complex✓ so that either the results become difficult to interpret✓ and communicate✓, … … or the model takes too long✓ or becomes too expensive to run✓.
Any shortcomings of the model should be clearly stated.✓✓
The model should be capable of subsequent development and refinement.✓✓
Q&A 14.9
ii) Describe briefly the main features that would be included in the calculations performed within the model and explain how the model would be used to enable you to make a report on the value of the existing business to the company. [7]
ii)
Main features
All future cashflows✓ from the existing business✓ would be projected by the model✓ …
allowing for cashflows arising from supervisory reserves✓✓ … … and from discretionary benefits✓, such as non-guaranteed surrender values✓.
Cashflow calculations need to allow for any interactions between assets and liabilities.✓✓
Cashflows arising from the exercise of policy options would need to be included.✓✓
Use of the model
To calculate the value of the profit from the existing business:
Model points would need to be chosen to represent the existing business.✓✓
Project the future cashflows from each model point✓✓, allowing for the impact of supervisory reserves✓ in order to assess the profit that can be transferred to shareholders✓ in each future year✓.
Discount the expected profit at an appropriate risk discount rate.✓✓
Scale up the results of each model point✓ and sum over all model points✓, to give the expected present value of the total profit✓ from the existing business✓.
Combine with the current assessment of the free assets attributable to shareholders✓ in order to get the total value of the profit✓.
Sensitivity✓ of the calculation would be assessed by recalculating using different values for all the relevant assumptions✓ required by the model (e.g. interest, mortality rates)✓.
When making these variations, the parameters would be changed in a way that reflects the expected relationship between them.✓✓
The effect of departures from the base assumptions used in the model can then be described in the report to the company.✓✓
Formula Approach
Formula approach The premium or contribution rate (CR) is set so that forecast income—or contributions—are equal to forecast outgo—benefits or claims and expenses.
{value of outgo} = {value of income} or
{value of outgo} {value of income}
= 1 Income and outgo must be discounted using suitable rates of interest.
Cj Approach
Cashflow approach For each model point, cashflows are projected and discounted at the risk discount rate. Premiums, contributions, or charges are found that satisfy the funding criteria. Cashflow items include premiums / contributions, expenses, claims or withdrawals, contribution to reserves and capital requirements, interest and tax, plus appropriate items for long-term products. Interactions between items should be allowed for.
Stochastic vs Det
Stochastic and deterministic models l Stochastic modelling is important for healthcare insurance due to the uncertainty around future incidence experience, in terms of number of claims and benefit amount.
l Parameters for economic assumptions may be set by risk neutral—market-consistent—calibration, or real-world calibration.
l The choice between a stochastic and deterministic model will depend on the product or benefit being modelled; a combination of the two may be used.
l Stochastic models may be more useful for modelling guarantees. l However, stochastic models may be complex, time-consuming, or difficult to understand.
l Both forms of model rely on the accuracy and validity of the data being used and suitability of the parameters.
Chapter question 4
State with reasons whether to use a deterministic or a stochastic model for the following purposes:
a) Assessing the estimated loss to your portfolio of PMI policies if there was an epidemic or pandemic, such as COVID-19
b) Estimating the expected value and variance of CI claims next year
[1.5]
(a)
Probably deterministic, as only one answer is required.✓✓
(b) Stochastic, as a variance is involved, which necessitates a distribution.✓✓
(c) Stochastic, as a variance will be needed to assess the likelihood of not being able to meet a specific fixed target.✓✓
Chapter question 4
State with reasons whether to use a deterministic or a stochastic model for the following purposes:
d) Renewal rates for PMI business if trying to assess the projected business volumes. [3.5]
(d) The problem with predicting renewal rates is that they are heavily influenced by economic and commercial factors.✓✓
For example, renewal rates can be influenced by:
* Economic conditions, especially those affecting employment✓✓
* Media publicity✓
* Comparison with competitors✓
* Selling practices✓
* Significant events✓, for example, economic recession✓, occurring in the past, lead to distortions in the past experience data✓, while future occurrences of such events are almost impossible to predict✓.
It is therefore difficult or impossible to devise a probability distribution for future renewal rates with any degree of confidence✓✓, which makes a stochastic approach doubtful✓.
The best approach would probably be a deterministic model for renewal rates, testing the effect of a whole range of possible outcomes.✓✓
