Modelling (18-19)

Question 1

State the

Requirements of a good model

Answer 1

Vivacious rabbits frolic, painting colorful jungles, including tiny dragons in caves.
* The model should be valid, rigorous enough for its purpose and adequately documented.
* The model should be capable of reflecting the risk profile of the products being modelled.
* The parameters should allow for all significant features of the business being modelled.
* The inputs to the parameter values should be appropriate to the business being modelled and take into account the economic and business environment in which it is operating.
* The workings of the model should be easy to appreciate and communicate. The results should be displayed clearly.
* The model should exhibit sensible joint behaviour of model variables.
* The outputs from the model should be capable of independent verification for reasonableness and should be communicable to those to whom advice will be given.
* The model must not be overly complex so that either the results become difficult to interpret and communicate or the model becomes too long or expensive to run, unless this is required by the purpose of the model.
* The model should be capable of development and refinement.
* A range of methods of implementation should be available to facilitate testing, parameterisation and focus of results.

Question 2

What is a model point

Answer 2

• underlying business being modelled will typically comprise a very wide rage of different policies
• need to create a manageable number of relatively homogenous groups
• each policy in a group should be expeted to produce similar results from model run
• since ‘representative’ policy is run though model and result is scaled up to give total result for set of policies
• ‘representative’ policy : model point

Question 3

Choosing model points

Answer 3

• adequeatly reflect the distribution of the business being modelled
• if model includes new business, actuary must decide what business volumes and business mix by product should be assumed.
• factors that influence sales volumes and persistency:
• ecomic morale
• government provision
• welfare
• tax
• demand for LTCI depends on political commitment

goverment can influence future take up of LTCI by influencing state provision. factors include the level of state benefits and rules on wealth requirements for state-benefits

Question 4

When should a parameter be included

Answer 4

If the decision reached would alter for different values of that parameter.

Question 5

Parameter values

Answer 5

• inputs should be appropriate to the business being modelled
• take into account special features of the company
• take into account economic and business environment
• model should exhibit sensible joint behaviour of model variables

Question 6

Communication and Verification

Answer 6

• Outputs should be capable of independent verification for reasonableness
• Output should be readily communicable to those to whom advice will be given

Output should be checked:
- recon with last valuation
- recon with last time model was run
- perform simple ratio checked on future years’ results
- construct a simple “back of the envelope”model using a few model points. Check full model’s output against this for order of magnitude errors

Question 7

Complexity vs time and cost

Answer 7

the model must:
- not be overly complex so that results are difficult to interpret and communicate
- not be too long or expensive to run (unless required by purpose)
- shortcomings should be clearly stated
- model should be capable of subsequent development and refinement

Question 8

What factors influence the number of model points chosen

Answer 8

VIT C CATS
- variability of contracts sold
- Importance of the investigation
- time available
- computer power and availability
- complexity of contracts in force
- age of the company
- Types of model - stochastic or deterministic
- sensitivity of the results using more or fewer model points

Question 9

Basic features of LI model

Answer 9

1. projecting cashflows and profit
2. Allowance for interactions
3. choosing between stochastic and deterministic
4. projection frequency and time period
5. allowing for guarantees and options

Question 10

Basic features of LI model

projecting cashflows and profit

Example: discretionary cashflows

Answer 10

model needs to allow for:
- all cash flows that may arise
which depends on premium and benefit structure
and other discretionary benefits
- cash flows arising from any supervisory requirement to hold reserves and solvency capital
these are notional cashflows, since it does not involve a physical exchange of money
- profit = change in the value of free assets over the year
free assets = assets - (supervisory reserve+solvency capital)

For example, in a model involving bonuses, the model will need to incorporate an algorithm to “decide” what bonuses should be awarded given the projected investment results. This algorithm will probably make reference to asset share, in which case the model would need to calculate projected asset shares for policies.

Question 11

Basic features of LI model

Allowance for interactions

Answer 11

Cashflows need to allow for interactions, especially where assets and liabilities are being modelled together.
- vital when model is stochastic - variables change yearly and ongoing responses need to occur automatically as each simulation is run
- model should be dynamic: A and L parts are programmed to interact as they do in reality

example: change in investment strategy in responce to changing market conditions

Question 12

Basic features of LI model

allowing for guarantees and options

Answer 12

Need to allow for:
- potential cashflows from such options
- implications of these options and guarantees for the supervisory reserves
- The ability to use stochastic models and simulations

Question 13

Basic features of LI model

choosing between stochastic and deterministic

Answer 13

Deterministic:
- will not give adequate info about the resilience of the company to , e.g., asset value fluctuations
- used for quick independent test to check reasonableness of stochastic model
- possible outcomes form a symmetric distribution and info is only required on expectation
- only one specific scenario is being tested
- Equivalence principle
single deterministic result based on average assumptions together with a series of further deterministic calcs on amended assumptions, may in simple cases be used to provide upper and lower bounds on the corresponding stochastic results

Stochastic
- preferable
- can assign prob distr to parameters
- positive liability can be calculated where a deterministic model might produce zero liability (cashflows includes min guaranteed benefit)
- parameters vary together as a dynamic set

Disadv:
- time and computing constraints
- sensity of the results to the assumed values of the parameters (spurios accuracy)

Nested stochastic model:
- one which requires stochastic projections within each stochastic simulation
- can be avoided with deterministic or closed-form approximation approach

Question 14

Basic features of LI model

projection frequency and time period

Answer 14

chose time period for cashflows, considering:
1. the more frequently cashflows are caluclated, the more reliable the output from the model
2. the less frequently the cashflows are calculated, the faster the model can be run and results obtained

anything more frequently than monthly would not produce a sufficient gain in accuracy compared to model run time

projection period is usually 3-5 years, anything beyond that would be exposed to the funnel of doubt

Question 15

Cailbration of stochastic models

Answer 15

For a stochastic model in which the economic assumptions vary, the following approaches can be used to set (calibrate) these parameters:
1. Risk neutral calibration
2. Real world calibration

Question 16

Cailbration of stochastic models

Risk neutral calibration

Answer 16

• market-consistent calibration
• used for valuation purposes
• particularly where there are options and guarantees
• focus is to replicate the market prices of actual finincial instruments as closely as possible
• using an adjusted risk neutral probability measure

method:
- choose a number of financial instruments
- usually derivatives
- model is built to project the cashflows from these instruments in a range of scenarios
- parameters are chosen such that the average PV of the cashflows is close enough to known market price

Question 17

Cailbration of stochastic models

Real world calibration

Answer 17

• typically used for projecting into the future
• e.g. calculating the appropriate level of capital to hold to ensure solvency under extreme adverse scenarios at a given confidence level
• focus is to use assumptions which reflect realistic long term expectations
• which also reflect observable real world probabilities and outcomes

method:
- determine model parameters using expectations of the future
- assumptions are then used to project values of A & L under each stochastic scenarios.

Question 18

Financial economic or market-consistent approach

Answer 18

• Assumes market-consistent values for parameters
• Assumed investment rate = RFR
  (Additional return from e.g. equities is cancelled out by increased risk)
• Asset valuation @ Market rate
• Liability valuation @ Current MV of RF assets that match liability CFs
• Problem: Assessing MV of non-financial aspects of the liability e.g. mortality

Question 19

Use of models

Answer 19

• pricing
• assessing return on capital
• assessing profitbaility on existing business
• projecting future supervisory solvency position

Question 20

Use of models - Pricing

Answer 20

• determining premiums or charging rates
• that will meet the company’s profit requirement
• marketability
• capital requirements
• assesing return on capital

Question 21

Use of models - Pricing

determining premiums or charging rates

Answer 21

• Model can be used to determine premium/charging structure for a new/existing product that will meet the LI company’s profit criteria
• Model points will be chosen to represent existing/new business
• Project CFs for each model point (making allowance for reserving/solvency margin requirements) based on assumptions
• Discount CFs at risk discount rate (RDR) – i.e. get EPV. RDR must allow for:
   Return required by company
   Level of statistical risk attached to the CF
• Set premium such that it fulfils profit criteria

Question 22

Use of models - Pricing

profit criteria

Answer 22

Profit criterion: single figure that tries to summarise the relative efficiency of different contracts with different profit signatures
- Profit signature: sequence of profits over time from inception to termination

3 criteria:
1. NPV
- most used
- disount profit signature using RDR
- the higher, the better
- assumptions: perfectly free and efficient capital market & RDR reflects riskiness
- subject to the law of diminishing returns
- doesn’t say anything about competition
- should be expressed as a proportion of something to be more useful
- % of initial sales cost: reflects the effort that would be expensed on selling a policy
- % of total discounted premiu: : since it relates to the size fo the market

2. IRR
   - highest rate or return at which NPV is zero
   - the higher the better
   - does not alwas agree with NPV
   - disadvantages:
   May not exist - if profit is made at the outset
   may not be unique - when there is more than one change in sign in the profit signature
   cannot be related to other measures (like with NPV)
3. DPP
   - policy duration at which the profits so far have a NPV of 0
   - useful when a company is eager to recoup initial capital in as short a time as possible
   - most importance for longer term policies with initial capital strains
   - will not usually agree with NPV as it ignores all future cashflows after the DPP

Question 23

Use of models - Pricing

marketability

Answer 23

Premiums and charges need to be considered for marketability

This might lead to reconsideration of:
* deign of product: Remove features to reduce riskiness or include to differentiate from competitors
* Distribution channel: if that would permit revision of assumptions or model
* profit requirement
- whether to proceed with marketing of the product

Question 24

Use of models - Pricing

capital requirements

Answer 24

By assessing the timing and amount of cashflows from the model, the impact on capital management could be observed and design of product could be changed if capital is a problem
* The net cashflows, scaled up for expected new business , will be incorporated into a full model office.
* Not each model point has to be profitable for overall profitability to be reached in aggregate

Question 25

Use of models - Pricing

assesing return on capital

Answer 25

Net cashflows from new business model could be grossed up, added with any one-off development costs to obtain total capital requirement, and compared to expected profits to determine the return on capital.

Question 26

Use of models - assessing profitability on existing business

Answer 26

• full policy data set may be used (modelling done on policy by policy basis)
• alternatively, model points could be used:
  -> Model points from previous assessments may be used as starting points
  -> then modified to allow for changes due to new business coming in and old business going off
  -> check suitability then apply model to each model point
• totalling accoss all polcies = expected profit from existing business
• useful to look at PVFP by:
  -> product
  -> product class
  -> Distribution channel
  -> subsidiaries , if applicable
• RDR should be less than for pricing since New business related risk is reduced

Question 27

Use of model: assessing solvency

Answer 27

• Measuring solvency: comparing the value of assets and liabilities
• amounts and types of capital needed depends on the amounts of liabilities and the inherent risks of those
• Need to project liabilities into the future, allowing for new business plans, to assess capital requirements.
• Ongoing solvency needs to be tested, taking into account management actions

Question 28

two ways of determining the values of assets and liabilities for solvency

Methods and disadvantages

Answer 28

1. Supervisory values
   values determined vir supervisory reporting purposes (does not consider future new business & does not allow for guarantees)
2. economic values
   values determined on the basis of the expected experience of the company - “market consistent” basis

Question 29

Static vs Dynamic solvency testing

Answer 29

Static solvency testing
* determining solvecny at a particular point in time

Dynamic solvency testing
* projection of company’s revenue account and balance sheet forward for a sufficient period of years
* So that the full effect of any potential risks become apparent
* full model office with model points reprenting the liability portfolio is required
* can be deterministic or stochastic
* stochastic: would be possible to calcualte the probability of ruin for company: assesing the prob that at some point in future, the company would become insolvent on supervisory or economic value basis
* consider whether projections will include expected future new business

Question 30

Two reasons why new business should be included in projections
and the disadvantages of doing so

Answer 30

1. Realism
   makes sense to project in accordance with the company is actually going to do
2. Prudence
   due to capital strain involved in writing new business, it will be more prudent to assume new business continues
   thereby testing the company’s ability to finance future new business strain without becoming insolvent

Disadvantages:
* levels and mix of new business are difficult to predict accurately
* future products are not all known now
* some may argue that ito per policy expenses it is more prudent to assume close to new business

Question 31

Sensitivities

Answer 31

1. Sensitivity to the choice of model point
   More likely an issue when there is a smaller number of model points
   Effect of a different model point choice should be assessed
2. Sensitivity to parameters
   Sensitivity analysis determines effect of mis-estimation (actual != expected) of parameter values:
   * Assess effect on output of model with varying parameter value
   * Allow for correlations between parameters
3. Sensitivity testing when pricing
   Will determine margins required in the parameters
   If the product profitability is overly sensitive to any factor – redefine product or take other measures
4. Sensitivity testing for business in force
   Results from sensitivity analysis will help quantify the effect of a departure from chosen parameter values when presenting the results
5. Alternative ways for allowing for risk
   * One way: RDR
   * Other way: use predetermined lower rate and assess effect on results of the models of statistical risk
   o When a probability distribution is used, it may be possible to derive analytically the variance of a parameter
   o A sensitivity analysis could be used as well

Question 32

Q: Re-launch regular premium UL EA. Steps in designing and pricing the product: MAMPORS

Answer 32

1. Collect market information
2. determine assumptions and criteria
3. create model points
4. perform profit test
5. Run model office
6. Consider risks
7. Amend charging structure