Embedded Options and Guarantees

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Embedded Options and Guarantees

• Rob van Leijenhorst (AAG), Jiajia Cui
• AFIR2003 colloquium, Sep. 19th. 2003

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Agenda

• Introduction
• Importance of Guarantees
• Recognizing Guarantees and the Embedded Options
• Valuation Methods
• Case Studies
• How to Win the Chess Game

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Introduction

• Traditional actuarial valuations / profit testing
• Guarantees are not explicitly priced
• No extra reserve for guarantees
• Markets meltdown
• Low interest rates
• Bearish equity markets
• Ernst Young investigations on Guarantee issues
• Global
• Netherlands

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Guarantees Matter

• Two Aspects
• The risk of failing to meet guaranteed
  obligations due to adverse market movements
• The risk of reduced shareholder returns due to
  poor market performance
• Catastrophic Lessons
• (Japan) Seven insurance company failures since
  1997, (Interest Rate Guarantees) SOA spring
  meeting, 2003
• (UK) Equitable Life closed new business for old
  policies with Guaranteed Annuity Option in 2000.
• (UK) 85bn / 258bn With-Profit funds have closed
  new business, (Interest Rate Guarantees in WP)
  FSA estimates 2003

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Recognize Embedded Derivatives
GUARANTEE PAYS MAXIMUM OF A OR B
COMPONENTS OF GUARANTEE COST
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Examples
SAMPLE CONTRACT
QUANTITY A
QUANTITY B
UK Traditional participating insurance with
guaranteed sums assured and reversionary
bonuses
Asset Share
Sum assured plus vested bonuses
Premium accumulated at the guaranteed rate
over the term of the contract
NL Unit-Linked contract with a
maximum of maturity benefit or
return of premium accumulated at a
guaranteed minimum crediting rate
Account Balance
Funds required to purchase the guaranteed
annuity using current terms
US Guaranteed Minimum Income Benefit (similar
to Guaranteed Annuity Option in the UK)
Account Balance
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Fair Value Accounting
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Fair Value/Option Pricing
Only When In-The-Money
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Not Explicitly
Not At All
Other
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Valuation Methods
TECHNIQUES TO VALUE GUARANTEES OPTIONS
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ASSUMPTIONS Arbitrage Free Complete Markets
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Replication
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• Pros Perfect Replication Hedging Valuation
• Cons limited to few cases limited by available
  financial instruments

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Stochastic

• Analytic solutions

• Pros accurate fast (for maturity guarantees)
• Cons Implementing multi-period guarantees
  resorts to numerical methods model dependent

• Lattice

• Pros Efficient numerical method
• Cons Difficulty with multi-randomness Model
  dependent

• Simulation

• Pros Accommodate complex cash flows,
  Multi-randomness
• Cons Computing time Model dependent

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Case studies by Simulations

• Why simulation?
• Complex cash flows, multi-assets
• Existing products
• Unit-Linked products
• With-Profit products
• Group pension contracts
• Existing investment strategies

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Case studies

• Contract conditions investment strategies
  determine the characteristics values of
  guarantees
• Stochastic Assets modelling
• The Correlated Black-Scholes Hull White Model
• Money market account, Stock account, Bond
  portfolio, Mix fund

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Case Study (1) Unit-Linked Contracts

• Minimum Rate of Return Guarantee (e.g. 4 per
  year)
• Maturity Profit-sharing

The insured entitles to the best of either the
full fund value or a guaranteed minimum amount at
maturity.
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Case Study (2) With-Profit Contracts

• Annual Profit-sharing (e.g. the excess return
  over 4 is added to the sum assured)
• Distribution ratio (80), margin (50bp)

Contract value
Fund value
In each period, the insured entitles to the best
of _at_4 or the excess return.
Deficit is enlarged!
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Case Study (2) With-Profit Contracts (cont.)

• Deficit compensation
• Conditional Profit-sharing

Contract value
In each period, if no deficit, the insured
entitles to the best of _at_4 or the excess return.
deficit
Deficit is limited!
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Numerical Results (1) Unit-Linked Contracts

• As of PV premiums
• Single premium v.s. regular premium

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Numerical Results (2) With-Profit contracts

• As of PV premiums
• Annual profit-sharing v.s. conditional
  profit-sharing

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How to Win the Chess Game

• Valuation Risk management
• What will be the capital requirement?
• How will balance sheet volatility be managed?
• What are the implications to new business
  pricing terms?
• Think Ahead of the Competition
• How Ernst Young can help?
• Identifying embedded option
• Identify reliability assets
• Building models for valuation and projection
• Solutions for managing balance sheet volatility
• Verifying the effectiveness of derivative hedges
• New product design

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Contacts

• Rob van Leijenhorst (AAG)
• Rob.van.leijenhorst_at_nl.ey.com
• Paul de Beus (Senior Manager)
• Paul.de.beus_at_nl.ey.com
• Jiajia Cui
• Jiajia.cui_at_nl.ey.com