Chapter 18-Models (1)

Question 1

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

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
+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
Back of the envelope model

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

Requirements/Features of a life insurance model:

Answer 5

model must allow for all cashflows that may arise
depends on contract’s nature, premium, benefit structure, discretionary benefits

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

Proper allowance needs to be made for guarantees and options

Allowance for interaction and correlation between variables

Question 6

What is a stochastic model?

For stochastic models compared to deterministic models:

State 3 advantages
State 2 disadvantages

Answer 6

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 7

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

Answer 7

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

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 8

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

Answer 8

Easier to explain (particularly to non-technical audience)

Easier to interpret/understand

Clearer which (economic) scenarios have been tested

Easier to design

Easier/shorter to run

Question 9

Describe 2 approaches to calibrating stochastic models of economic variables

Answer 9

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 10

Two types of variation that should be considered when performing sensitivity testing

Answer 10

Model Points (especially if a small number of model points are used)

Parameters (Including the effect of correlations between parameters)