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Practical stochastic modelling for life insurers
Philippe GuijarroMike White
1 December 2003
The Glasgow Moat House
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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.
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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
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Part One
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Background to Stochastic Modelling
What is stochastic modelling?
How does it work?
Why is it so important?
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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)
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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
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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
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Why do we need simulation?(example for with profits guarantees)
Value of guarantees
Bonus strategy Investment strategy
Solvency
Complex interactions!!
Economy
Lapse rates
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Worked example
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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
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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
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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
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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
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Part Two
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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)
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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)
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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)
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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?
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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
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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
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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?)
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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
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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
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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
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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