Practical stochastic modelling for life insurers

Philippe GuijarroMike White

1 December 2003

The Glasgow Moat House

Purpose of this presentation

To provide an understanding of :

1) The importance of stochastic modelling for Life Insurers

2) The method by which UK insurers can create and use stochastic modelling functionality, and the numerous practical issues which will need to be managed.

Introduction

Part One Overview of stochastic modelling Uses of stochastic modelling for UK Life Insurers

Part Two Likely direction of stochastic modelling Practical aspects of building stochastic models

Part One

Background to Stochastic Modelling

What is stochastic modelling?

How does it work?

Why is it so important?

Reasons for stochastic modelling

Valuing one-sided payoffs (e.g. with profits business) Setting strategy (e.g. assessing investment

strategies) Managing the business (e.g. measuring performance

in fair manner) Regulatory (e.g. ICAS)

What is stochastic modelling?

Considering distributions of variables Different approaches

Numerical methods (e.g. Monte Carlo modelling) Closed form solutions (e.g. Black-Scholes)

For different purposes: Market consistent Realistic future experience

Background to Stochastic Modelling

Better to describe as Asset Liability Modelling (ALM) Stochastic element comes from selection of

economic scenario generator And certain demographics (e.g. interaction between

lapses and market falls) Building Asset Liability Model accounts for vast

majority of development work And involves many practical issues

Why do we need simulation?(example for with profits guarantees)

Value of guarantees

Bonus strategy Investment strategy

Solvency

Complex interactions!!

Economy

Lapse rates

Worked example

Product details

Unit linked endowment: 10 year term Premium £1,000 pa Death benefit is £10,000 Guaranteed maturity value £10,000 On survival, gets higher of guaranteed maturity value

and unit fund Unit funds invested in well diversified portfolio of

equities

Investment returns on equity index

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

70%

1 2 3 4 5 6 7 8 9 10

Probability of guarantee biting

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2 4 6 8 10

Deterministic (EV) vs stochastic (FV)

-600

-400

-200

0

200

400

600

0- 0+ 1 2 3 4 5 6 7 8 9 10

EMBV

-FV

Part Two

Where UK insurers are

Major UK With Profit offices expected to produce RBS results using asset liability modelling

Other needs (IFRS, Twin Peaks, Internal capital/risk management) Various stages of development (some very far advanced, most

adapting to rapid change in regulation) Modelling platform selected Building/extending functionality Smaller insurers approach (incl. NP/UL offices)

Likely direction of asset-liability modelling (ALM)

All major UK companies using ALM for With Profit valuation Also for other financial options/guarantees (e.g. GAO on Unit Linked) Convergence/acceptance of certain economic scenario generators Individual companies to justify their use of assumptions Output from model used to improve internal management of risks

(development versions) Also production versions used to produce regular reporting results

(Realistic Balance Sheet, International Financial Reporting Standards)

Practical aspects

Defining the required structure Building an asset liability model Using asset-liability functionality Application of the model Link with industry requirements (PSB, IAS, Realistic Balance Sheet)

Defining the required structure

Initial questions What is the purpose of the model? What existing systems/processes should be re-used? What level of accuracy is required? Which parts of the business should be modelled? Which are the essential deliverables? How much flexibility on resources, budget and timetable?

Defining the required structure

Liability Class n

Modular Model Design

Scenario Generator Model Report Model

Liability Model

Liability Class 1

Liability Class 2

…….

Asset Model

Corporate Model

…….Asset Class

2Asset Class

1Asset Class

n

Building an asset liability model

Systems, data and support

Specification and decision rules

Stochastic assumptions

Adapting to unexpected issues

Testing and Reasonableness

Interpreting, explanation and reporting

Using stochastic functionality

Introducing the economic scenario generator

Lots of different models – which one to use?

Likely that position will continue to develop

Essential to have flexibility to use different ESG

Also need to consider building in stochastic functionality for certain demographics (lapses, mortality?)

Considerations in choice of generator

Market consistency?

Arbitrage free?

Mean reversion / Fat tails

What assets to model?

Auditability / easy to explain?

Continuous / discrete?

.............. depends on liabilities and purpose

Application of the model

Stochastic capability adds extra dimension

Unlimited reports/results

Effective communication essential

Standard Reporting Chart

0

5

10

15

20

25

10,000 simulations

Cost of guarantee

(£m)

(sorted by size)

95th percentile

Link with industry requirements (PSB, IAS, Realistic Balance Sheet)

Market consistent modelling vs real world modelling – different ESGs?

Timetable

Flexibility

Documentation & use of model results in managing the business

Conclusion

Stochastic modelling is a big investment

Major insurance companies must have functionality

Provided designed and managed properly, can cover a number of reporting requirements

Understanding and communication of results critical