Ch 18: Models 1

Question 1

Summary Card

Answer 1

• Prime objective of models
• Types of models
• Requirements of models
• Stochastic & deterministic models

Question 2

State the prime objective in building a life insurance company model (2)

Answer 2

1. Enable actuary to give appropriate advice in company…
2. …so that it can be run in a sound way

Question 3

State the requirements of a good model (14)

Answer 3

1. Valid for purpose
   
   • deterministic vs stochastic
   • includes all notable features of what is being modelled
2. Rigorous
   
   • realistic results under wide range of circumstances
3. Well documented
   
   • audit trail, key assumptions/approximation
4. Reflect risks being modelled
5. Components used allow for material aspects being modelled
   
   • structural components:
   • parameters: only include param if results differs for different values of the parameter
6. Parameter values appropriate
   
   • for particular business
   • general environment, account for special features of company/economic environ
7. Sensible joing behaviour of variables eg:
   
   1. ​higher expense inflation => higher claims inflation
   2. higher claims rates => higher reinsurance recoveries
   3. higher inflation => higher (nominal) bond yields, equity returns?
8. Easy to
   
   1. Understand/appreciate model
   2. Communicate model
9. Output reasonable able to independent verify reaonableness
   
   1. Reconcile with supervisory valuation
   2. Reconcile with results from last run
   3. Ratio checks on future results
   4. Back of the envelope model
10. Output communicable
    
    1. to those who advice will be given to
    2. mentioning underlying method, critical assumptions
11. Results displayed clearly
12. Not overly complex to
    
    1. ​understand
    2. explain/communicate
    3. expensive to run
13. Able to develop/refine over time
14. Dynamic: assets and liabilities
    
    1. ​assumptions used to model assets/liabitlies must be consistent
    2. interactions between assets/liabilities modelled

Question 4

We’ve already covered the basic requirements of a good model.

List the general features of a life insurance company model specifically (5)

Answer 4

1. Model may be used to model different types of business
2. Model should project all cashflows that may arise
3. Allow for interactions/corellations between variables (dynamic links; joint sensible behaviour)
4. Guarantees/options should be propertly allowed for; stochastic model best for this
5. Projection frequency/time period

Question 5

List the 4 different types of life insurance company models (that differ in the policies that are included in the model).

Briefly descibe what each model does

Answer 5

1. Profit testing model
   
   • projects expected cash and profit flows on policies from date of issue
   • key for pricing/product design
   • 2. New business model
   • projects all expected cash and profit flows arising from future sales of new business
   • useful for assessing future capital requirements for new business/overall return on capital achieved from future sales
   • 3. Existing business model
   • cash & profit flor projection from all existing business company has in force at particular time point
   • important for assessing intrinsic value of existing business and testing solvency of company’s existing business
   • 4. Full model office
   • sum of new and existing business model
   • of fundamental importance in assessing impact of future maangement decisions on company’s future financial development

Question 6

Features of a life insurance model:

• Projecting cashflows/profit (3)

Answer 6

Projecting cashflows/profit

1. model must allow for all cashflows that may arise
   
   • depends on contract’s nature, premium, benefit structure, discretionary benefits
   • 2. supervisory reserves and solvency requirement (allow for cashflows arising from supervisory need to hold reserves/solvency capital)
   • real cashflows
     
     • premiums, investment income, payments to policyholders, commission to agents, expenses, tax
   • notional cashflows
     
     • fund establishment of reserves, by contributing money to reserves from cashflow or initially from company’s free assets
     • this increase in reserves is negarive from company’s perspective
     • at maturity/claim, reserves will be released to help pay appropriate benefit => decrease in reserves positive
     • 3. supervisory solvency capital
   • ​In addition to supervisory reserve, might be minimum supervisory solvency capital requirement to cover.
   • policy cashlfo might also need to fund establishment of solvency margin.
   • required solvency margin included in value of reserves

Question 7

Features of a life insurance model:

• allowing for interactions (2,5)

Answer 7

Cashflows need to allow for any interactions, particularly where assets and liabilities are being modelled together.

1. Dymaic model (asset/liability parts programmed to interact as in real life
   
   • investment return and bonus rates
   • supervisory reserves & projected investment conditions
   • investment strategy response to changing conditions
   • 2. Links are important
        1. for all models, but
        2. particularly for stochastic models, as variables are changing yearly and ongoing response need to occur automatically as each simulation is run

Question 8

Features of a life insurance model:

projection frequency and time period

(3)

(5)

Answer 8

• Frequency
  
  • more frequent cashflows calculation => more reliable output
  • less frequent cashflow calculation faster model is run
  • usually monthly
  • • Period
  • Whole company models
    • projection period chosen normally 3…5 years
    • anything more expose to doubt, especially regarding level and mix of new business,
    • but may usefully indicate significant trends, especially regarding solvency.
  • Individual product cashflows for profit testing purposes the projection period used will be the policy term.

Question 9

Features of a life insurance model:

• allowance for guarantees/options (3)

Answer 9

• Where health options exist (e.g. option to effect a new term assurance contract without providing further evidence of health), the potential cashflows from such options need to be allowed for.

1. Allow for effect on supervisory reserves
2. Allow for stochastic models/simulations
   
   1. …where appropriate, in order to assess impact of financial guarantees (e.g. minimum maturity guarantees)

Question 10

State 5 advantages of deterministic models compared to stochastic models (5)

Answer 10

1. Easier to explain (particularly to non-technical audience)
2. Easier to interpret/understand
3. Clearer which (economic) scenarios have been tested
4. Easier to design
5. Easier/shorter to run

Question 11

Give examples of circumstances in which deterministic models might be appropriate (4)

Answer 11

1. If similar results possible as if stochastic projection were used.
   
   • Possible outcomes form a symmetric distribution/information and information only required on the expectation, or
   • specific scenario being tested within simple cashflow model
2. Quick, independent test is required to see that the results of a stochastic projection are reasonable
3. To provide upper and lower bounds
4. To avoid nested stochastic model

Question 12

What is a stochastic model?

For stochastic models compared to deterministic models:

• State 3 advantages
• State 2 disadvantages

Answer 12

• A stochastic model is one in which we assign probability distributions to one or more unknown parameters.

Advantages

1. Distribution of outcomes (not just single outcome) because can prob distribution to one/more unknown future parameters
2. Positive liability can be calculated where deterministic approach might otherwise produce zero liability e.g. costing options and guarantees
3. Interactions explicitly modelled i.e parameters may be assumed to vary together

Disadvantages

1. Time and computing constraints
2. Possible spurous accuracy i.e. results very senstitive to (deterministically chosen) assumed values of parameter(s) involved

Question 13

Describe 2 approaches to calibrating stochastic models of economic variables

(5)

(4)

Answer 13

Risk neutral/market-consistent

• market-consistent: typically used for valuation purposes, particularly where there are options/guarantees
• focus: attempt to replicate market prices of financial instruments as closely as possible using risk neutral probability measure
  
  • choose number of financial instruments for which price is known
  • build model than can project cashflows from these instruments in a range of scenarios
  • parameters are chosen such that average PV of cashflows from modelled simulations is sufficiently close to known market price

​Real world calibrations

• typically used for projecting in future e.g. for calculating appropriate level of capital to hold to ensure solvency under extreme adverse future scenarios at a given confidence level
• focus: use assumptions according to realistic ‘long-term’ expectations and which consequently also reflect onbservable real world probabilities/outcomes
  
  • determine model parameters using expectations of future
  • assumptions used to project the values of assets/liabilities under each stochastic scenario