Chapter 12 - modelling

Question 1

What are the two main approaches to modelling for pricing?

Answer 1

1. cashflow approach

2. equation of value / formula approach

Question 2

Models may also be defined by the types of business they are modelling

Answer 2

1. single policy profit test model - projects expected cash and profit flows from a single policy from date of issue
2. new business model - this projects all the expected cash and profit flows from future sales of new business
3. existing business model - this projects all the expected cash and profit flows arising from exiting business at a particular time
4. full model office - this is essentially the sum of new business model and existing business model

Question 3

Main uses of models

Answer 3

1. costing and reserving for options
2. model office - new business projections, EVs, solvency, takeovers
3. reserves - statutory and management accounting
4. pricing - profit, premium rates

Question 4

What is a model point?

Answer 4

A model point is a data record that is fed into the computer as input for the modelling program. It will represent either a policy or group of policies, containing data on the most important characteristics of the policy.

Question 5

Requirements for a good model

Answer 5

VARIABLE CRISPS CARDS + EEL

• valid
• adequately documented
• rigorous for its purpose. produces realistic results for a wide range of circumstances
• input parameter values are appropriate and includes all necessary input parameters to reflect the characteristics of the product
• assumptions reasonable
• behaviour reasonable
• length of run time not too long / expense not too high
• easy to understand
• communicable workings and output
• reflects risk profile of product being modelled
• independent verification of output
• sensible joint behaviour of variables
• parameters allow for significant features
• simple but retains key features
• clear results
• a range of implementation methods
• refinable and re-developable
• dynamics between assets and liabilities

Question 6

Requirements for a good health insurance model

Answer 6

CRISSP

• needs to allow for all the cashflows that may arise, which depend on the nature of the contract, in terms of premium and benefit structure and any discretionary benefit such as options to convert, extend or increase cover without evidence of health
• allow for cashflows arising from any supervisory requirement to hold reserves and maintain an adequate margin of solvency
• 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 assets and liabilities are being modelled together
• the ability to use stochastic models and simulations needs to be allowed for where appropriate e.g. to simulate claims distribution

Question 7

Features of deterministic modelling

Answer 7

• each of the parameters has a fixed value
• the model produces the result 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

Question 8

Features of a stochastic modelling process

Answer 8

• some of the parameters 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
• the model produces results in the form of a probability distribution

Question 9

Why is stochastic modelling more important for healthcare insurance than for pure life insurance?

Answer 9

• With healthcare insurance products, the future incidence experience is far less easy to predict.
• The added difficulty lies with the potential benefit amount, which may vary by policy specified inflation (LTCI), medical inflation (PMI), by changes to medical protocols (PMI) or other factors
• with such uncertainty and hence volatility of cashflows, it is important to be able to project the distribution of possible future outcomes

Question 10

When is a stochastic model valuable?

Answer 10

• when you are trying to assess the impact of guarantees
• when the variable of interest does have a reasonably stable and predictable probability distribution
• for indicating the effect of year-on-year volatility on risk
• for identifying potentially high risk future scenarios

Question 11

Disadvantages of stochastic modelling

Answer 11

• time and computing constraints (so stochastic modelling work might be done with a very simplified version of the model)
• the sensitivity of the results to the assumed values of the parameters involved. This can lead to spurious accuracy

Question 12

Calibration of stochastic models

Answer 12

• risk neutral (market-consistent) calibration

- real world calibration

Question 13

Market-consistent calibration

Answer 13

• for valuation purposes, usually where options and guarantees are involved.
• aim to replicate the market price of financial instruments
• the idea is that if the model can closely reproduce the market price for quoted assets, then they should be able to closely reproduce the market prices for unquoted assets and liabilities
  1. choose a number of financial instruments for which you know the price
  2. a model is then built that projects the cashflows of these instruments under a range of scenarios
  3. the parameters are then chosen in such a way that the average present value of the cashflows from the modelled simulations is sufficiently close to the known market price

Question 14

Real world calibration

Answer 14

• usually used for projecting into the future e.g. determining the appropriate amount of capital to hold to ensure solvency under extreme adverse scenarios at a given confidence level.
• focus is to use assumptions that reflect realistic long-term expectations and that consequently also reflect observable real world probabilities and outcomes
• determine model parameters using our expectations of the future

Question 15

Sensitivity to choice of model point

Answer 15

• if adequate set of model points has been chosen, shouldn’t be necessary to test for model point error
• effect of a different choice should be assessed if less than ideal number of model points has been assumed
• if a large number of runs are required to test thoroughly the various parameter sensitivities, then the model might be recreated with a much smaller number of model points

Question 16

Sensitivity to parameters

Answer 16

• the effect of mis-estimation of parameter values can be assessed by carrying out sensitivity analysis
• assessing the effect on the output of the model of varying each of the parameter values
• correlations between parameters should be allowed for
• sensitivity analysis is very important in determining the range in which the best estimate will probably lie
• allows you to compare the relative financial impact of the uncertainty that is associated with each parameter estimate

Question 17

Uses of sensitivity

Answer 17

• sensitivity testing on a deterministic basis can be used to help determine the margins that may be necessary in the parameter values of pricing
• may be useful in determining appropriate margins in respect of potential adverse future experience, and in calculating additional risk margins, global reserves or capital requirements
• can be used to determine the variance of profit or of the return on capital for any business being modelled. Quantify the effects of departure from the chosen parameter value when presenting the model to the company. Can be assessed analytically where a probability distribution can be assigned to a parameter.

Question 18

Drawbacks of formula approach (most of them are only of major concern when pricing long-term contracts)

Answer 18

• does not allow for proper timing of events
• does not allow for the accumulation of reserves
• does not properly allow for capital needs (it is not possible to allow for desired rate of return required by shareholders on their capital)
• does not allow for the impact of negative cashflows in any period (assumes borrowing rate is same as discount rate)
• doesn’t allow for separate inspection of premium-related cashflows or claim-related cashflows
• doesn’t allow easily for variation of assumptions over time
• doesn’t allow for changes in assumed future experience and cannot be used to measure sensitivity of profit to such variations
• cannot easily allow for more complicated product structure e.g. unit-linked

Question 19

Cashflow approach to pricing (not generally used for PMI)

Answer 19

• a number of model points will be chosen to represent the expected new business under the product.
• in the case of an existing product, the profile of the existing business, modified to allow for any expected changes in the future, can be used to obtain the model points (existing business will be that recently written)
• for a new product, the profile of a similar existing product combined with marketing department advice would be used
• for each model point, cashflows will be projected, allowing for reserving and solvency capital requirements, using a set of base values for the parameters in the model
• net projected cashflows will then be discounted at the RDR
• the premium or charges for the model point can be set so as to produce the profit required by the company
• alternatively, the desired level of profitability can be reached in aggregate
• if certain model points aren’t profitable, the aggregate profitability of the business is then exposed to changes in mix
• once acceptable premiums have been determined for the model points, premiums for all contract variations can be determined. The model produced can then be applied to other model points.

Question 20

Other uses of cashflow techniques for PMI

Answer 20

• PMI business incurs high expenses when a policy is first sold compared with its renewal, and it is usual to spread the cost of the high initial expense over the expected number of renewals of the policy. Cashflow modelling is sometimes used to quantify this.
• assess adequacy of proposed premium s over a longer term.

Question 21

Cashflow approach to assessing profitability

Answer 21

• full policy data may be used or model points may be used
• model points used for previous assessment may form a starting point, modified to allow for changes due to new business taken on by the company
• or redo model point generation process
• suitability of model points used should be checked.
• where profitability being assessed at same time as supervisory reserves are calculated, one check is to use model points to determine the supervisory reserve and then compare this value with the published value
• discount CF at RDR
• RDR usually less than that used for product pricing because some of the risks are reduced (new business volume and mix)
• total across all policies

Question 22

Use of cashflow approach in assessing profitability

Answer 22

• can be useful to look at PVs of future profits broken down by product, product class, distribution channel, subsidiaries to compare contribution to profitability
• prime use is as part of calculation of the insurance company’s EV (sum of company’s existing free assets net of liabilities + future profits expected from in-force business)

Question 23

Cashflow approach to assessing return on capital

Answer 23

• the net cashflows for model points can be grossed up for expected new business and to assess the amount of capital that will be required to write the business
• to this can be added any one-off development costs
• this gives the total capital requirement which can be compared with the profits expected to emerge so as to determine return on capital

Question 24

Cashflow approach to determining capital requirements

Answer 24

• a full model office may be used in order to determine the capital required to write new business.
• the net cashflows in respect of the model points, appropriately scaled up for new business, will be incorporated into a model of the business of the whole company
• the actuary can thus assess the impact in capital management terms of writing the product by observing the modelled amount and timing of the cashflow
• if capital is a problem, this may lead to reconsideration of design

Question 25

Disadvantages of writing capital intensive business

Answer 25

all other things being equal, capital intensive business will: - give a lower rate of return - reduce the company's apparent financial strength (usually measures as free assets in relation to the reserves) - increase the opportunity cost of capital - be more exposed to the risk of adverse experience, because it would be more diversified if it uses capital to finance a large number of non-capital intensive policies - lead directly to a problem with statutory solvency - weaken company's resilience to falls in the value of assets

Question 26

States in LTCI

Answer 26

- capable premium payers - lives incapacitated in the deferred period - lives becoming claimants following deferred period - lives moving to further states of incapacity - lives dying - lives recovering, reverting to premium payers

Question 27

Multi-state modelling for pricing

Answer 27

- requires determination of the proportion of lives in each status, using relevant duration-based intensities - the value of claims outgo will depend on the number of lives within the sub-cohorts, in a given month, multiplied by the relevant average sum - this will be balanced against premiums for premium-paying state plus investment income less expenses - transition intensities applied to each status to determine the numbers appropriate to various cells for the next month - in practice, combination of sub-cohorts and reduction of number of transition intensities is required

Question 28

Multi-state modelling for reserving/reporting

Answer 28

- similar tools will apply but assumptions underpinning the parameters will need to be adjusted in accordance with the purpose for which the estimates are calculated.

Question 29

What does each model require?

Answer 29

- policy liability model - expense model - asset model

Question 30

Product liability model

Answer 30

- a product modelling program that projects cashflows for policies over their future term to expiry - will take model points (representing new and existing business) and parameters (claim incidence, withdrawal rates) as inputs - projects forward, to the end of each future year of the projection period, the in-force portfolio of policies - calculate supervisory reserves and required solvency capital at the end of each projection year - projects total cashflows that arise each year, which will enable projected assets to be calculated for each year end (and annual profit)

Question 31

Expense model

Answer 31

- the expense model for the full model office would need to calculate the total expected expenses of the company - the expense components for the single policy, new and existing business models would need to be restricted to the expenses relating to those parts of the business being modelled - modelling of fixed overheads may be difficult, especially for profit test and new business models. For the full model office, fixed overhead expenses should be modelled globally.

Question 32

Asset model

Answer 32

Will vary in complexity according to the overall type pf model and its purpose - asset model for profit test will commonly consist of future total annual expected investment return only - at other extreme, if using a full model office to assess the company's future investment strategy, we would need a stochastic model capable of producing an appropriate distribution for each asset class, that projected income and gains separately, and that reflected mix of assets held