Ch 18: Models 1

Question 1

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

Answer 1

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

Question 2

State the requirements of a good model (14)

Answer 2

1. Valid for purpose
   
   • deterministic vs stochastic
   • includes all notable features of what is being modelled
2. Rigorous
   
   • produces realistic results under a wide range of circumstances
3. Well documented
   
   • audit trail, key assumptions/approximation
4. Reflect risk profile of the product being modelled
5. Inputs to the parameter values should be appropriate to the business being modelled and take into account the economic and business environment in which its operating
   
   • structural components:
   • parameters: only include parameter 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 environment
7. Sensible joint 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 3

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

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

Answer 3

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

Question 4

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 4

1. Single Policy Profit testing model
   
   • projects expected cash and profit flows on policies from date of issue
   • key for pricing/product design
   • Output= annual emergence of profit
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 management decisions on company’s future financial development
   • Output= The company’s supervisory balance sheet and the projected distributions of profit

Question 5

Features of a life insurance model:

• Projecting cashflows/profit (3)

Answer 5

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- the flow does not involve a physical exchange of money
     
     • fund establishment of reserves, by contributing money to reserves from cashflow or initially from company’s free assets
     • this increase in reserves is negative from company’s perspective
     • at maturity/claim, reserves will be released to help pay appropriate benefit => decrease in reserves is positive from company’s perspective
3. supervisory solvency capital
   
   • ​In addition to supervisory reserve, might be minimum supervisory solvency capital requirement to cover.
   • policy cashflow might also need to fund establishment of solvency margin.
   • required solvency margin included in value of reserves

Question 6

Features of a life insurance model:

• allowing for interactions (2,5)

Answer 6

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

1. Dynamic model - assets and liability parts programmed to interact as they do in reality
   
   • 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 7

Features of a life insurance model:

projection frequency and time period

(3)

(5)

Answer 7

• 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 8

Features of a life insurance model:

• allowance for guarantees/options (3)

Answer 8

• 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 9

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

Answer 9

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 10

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

Answer 10

1. If similar results could be obtained as if a full 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 with sensitivity testing
   - in order to get an approximation to a stochastic result
4. To avoid nested stochastic model- one which requires stochastic projections within each stochastic simulation.
   
   • A deterministic or closed-form approximation approach may be needed

Question 11

What is a stochastic model?

For stochastic models compared to deterministic models:

• State 3 advantages
• State 2 disadvantages

Answer 11

• 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) - method allows a probability distribution to be assigned to one/more unknown future parameters
2. Able to cost options and guarantees - Positive liability can be calculated where deterministic approach might otherwise produce zero liability
3. Interactions explicitly modelled i.e parameters may be assumed to vary together as a dynamic set –> useful for modelling with-profits business

Disadvantages

1. Time and computing constraints
2. Possible spurous accuracy i.e. results very senstitive to the (deterministically chosen) assumed values of parameter(s) involved
   – we should only use stochastic modelling when the variable can be reliably modelled by a well-defined probability distribution.

Question 12

Describe 2 approaches to calibrating stochastic models of economic variables

(5)

(4)

Answer 12

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 which reflect realistic ‘long-term’ expectations and which consequently also reflect observable “real world” probabilities and outcomes
  
  • determine model parameters using expectations of future
  • assumptions used to project the values of assets/liabilities under each stochastic scenario