Chapter 18 - Models

Question 1

State the prime objective in building a life insurance company model

Answer 1

Enable actuary to give appropriate advice in company…

…so that it can be run in a sound financial way

Question 2

State the requirements of a good model (14)

Answer 2

• Valid for purpose
• Rigorous- realistic results under wide range of circumstances
• Well documented - audit trail, key assumptions/approximation
• Reflect risks being modelled
• Parameters/components used allow for material aspects of business being modelled
• Parameter values appropriate - for particular business and the general environment
• Sensible joint behaviour of variables eg:
  +higher expense inflation => higher claims inflation
  +higher claims rates => higher reinsurance recoveries
  +higher inflation => higher (nominal) bond yields, equity returns?
• Easy to understand/appreciate model
• Easy to communicate model
• Results displayed clearly
• Output reasonable able to independent verify reasonableness
  +Reconcile with supervisory valuation
  +Reconcile with results from last run
  +Ratio checks on future results
• Not overly complex to
  +understand
  +explain/communicate
  +expensive to run
• Ability to develop/refine over time

Question 3

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

Answer 3

• Model may be used to model different types of business
• Model should project all cashflows that may arise
• Allow for interactions/correlations between variables (dynamic links; joint sensible behaviour)
• Guarantees/options should be properly allowed for; stochastic model best for this
• 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)

Answer 4

Profit testing model
* projects expected cash and profit flows on policies from date of issue
* key for pricing/product design

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

Existing business model
* cash & profit for 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

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

Question 5

What is a stochastic model?

For stochastic models compared to deterministic models:

State 3 advantages
State 2 disadvantages

Answer 5

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

Advantages

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

Disadvantages

• Time and computing constraints
• Possible spurious accuracy i.e. results very sensitive to (deterministic chosen) assumed values of parameter(s) involved

Question 6

Give examples of circumstances in which deterministic models might be appropriate (5)

Answer 6

• the actuary is satified that similar results could be obtained as if a full stochastic projection was used
• specific scenario being tested within simple cashflow model
• Quick, independent test is required to see that the results of a stochastic projection are reasonable
• To provide upper and lower bounds
• To avoid nested stochastic model

Question 7

Describe 2 approaches to calibrating stochastic models of economic variables

Answer 7

• Risk neutral/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
• 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 observable real world probabilities/outcomes

Question 8

What is the financial economic or market-consistent approach

Answer 8

Financial economic approaches to modelling insurance business generally seek to set future unknown parameter values so as to be consistent with market values, where a corresponding market exists