Embedded Options and
Guarantees
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Embedded Options and Guarantees
Rob van Leijenhorst (AAG), Jiajia Cui
AFIR2003 colloquium, Sep. 19th. 2003
Agenda
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2
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
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Traditional actuarial valuations / profit testing
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Markets meltdown
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Low interest rates
Bearish equity markets
Ernst & Young investigations on Guarantee issues
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3
Guarantees are not explicitly priced
No extra reserve for guarantees
Global
Netherlands
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Guarantees Matter
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Two Aspects:
1. The risk of failing to meet guaranteed obligations due to adverse
market movements
2. The risk of reduced shareholder returns due to poor market
performance
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Catastrophic Lessons
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4
(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
Quantity
B
Quantity
A
5
COMPONENTS OF
GUARANTEE COST
Excess B-A
Quantity
A
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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
NL
Unit-Linked contract with a
maximum of maturity benefit or
return of premium accumulated
at a guaranteed minimum
crediting rate
Account Balance
Premium accumulated at
the guaranteed rate over
the term of the contract
US
Guaranteed Minimum
Income Benefit (similar to
Guaranteed Annuity Option
in the UK)
Account Balance
Funds required to purchase
the guaranteed annuity
using current terms
6
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Fair Value Accounting
2% 3%
14%
Fair Value/Option Pricing
Only When In-The-Money
6%
Not Explicitly
Not At All
Other
76%
7
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Valuation Methods
TECHNIQUES TO VALUE
GUARANTEES & OPTIONS
O p tio n
P r ic in g
T e c h n iq u e s
ASSUMPTIONS
Arbitrage Free & Complete Markets
8
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Replication
Liability Cashflows
Guarantee Costs
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Normal Benefits
1
2
3
TIME
Replicating Asset for Normal Benefits
4
5
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TIME
1
2
3
4
5
4
5
Replicating Asset for Guarantee Costs
TIME
1
2
Value of
Liability
Cashflows
9
3
Pros:
Perfect Replication;
Hedging + Valuation
Cons:
limited to few cases;
limited by available
financial instruments;
Total Value of
Replicating
Assets
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Stochastic
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Analytic solutions
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Lattice
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Pros: Efficient numerical method
Cons: Difficulty with multi-randomness; Model dependent
Simulation
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10
Pros: accurate; fast (for maturity guarantees)
Cons: Implementing multi-period guarantees resorts to numerical
methods; model dependent
Pros: Accommodate complex cash flows, Multi-randomness
Cons: Computing time; Model dependent;
Motivation & Background
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10
Case studies by Simulations
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Why simulation?
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Existing products
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Complex cash flows, multi-assets
Unit-Linked products
With-Profit products
Group pension contracts
Existing investment strategies
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Case studies
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Contract conditions + investment strategies
determine the characteristics & values of guarantees
Stochastic Assets modelling
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12
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
regular premium Unit-Linked contract (2 scenarios)
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Minimum Rate of
Return Guarantee
(e.g. 4% per year)
Maturity
Profit-sharing
20
18
profit
16
14
12
shortfall
10
The insured entitles to
the best of either the
full fund value or a
guaranteed minimum
amount at maturity.
8
6
4
2
0
13
0
20
40
60
80
contract maturity (months)
100
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120
140
Case Study (2): With-Profit Contracts
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Annual Profit-sharing
(e.g. the excess return
over 4% is added to the
sum assured)
Distribution ratio (80%),
margin (50bp)
single premium With-Profit Contract
(80% distribution ratio, no deficit compensation) (on stock)
7
stock fund
contract
6
Contract
value
5
Fund value
4
In each period, the insured
entitles to the best of @4%
or the excess return.
3
2
Deficit is enlarged!
1
0
5
10
15
20
contract maturity
14
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25
30
Case Study (2): With-Profit Contracts (cont.)
single premium annual guarantee with deficit deduction and profit-sharing (on stock)
25
deficit
contract
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Deficit compensation
Conditional Profitsharing
20
15
In each period, if no deficit,
the insured entitles to the
best of @4% or the excess
return.
Deficit is limited!
15
Contract
value
10
deficit
5
0
0
5
10
15
20
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25
30
Numerical Results (1): Unit-Linked Contracts
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As % of PV premiums
Single premium v.s. regular premium
(UL) maturity guarantee on Stock
0,2
IRG
0,15
single prem
0,1
regular prem
0,05
0
0
10
20
30
40
contract maturity
16
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Numerical Results (2): With-Profit contracts
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As % of PV premiums
Annual profit-sharing v.s. conditional profit-sharing
(WP) yearly premium annual guarantee
on Mix Fund (80%B 20%S)
0,5
0,4
buffer(80%dis)
margin(25bp)
0,3
0,2
deficit
compensation
0,1
0
0
17
10
20
30
40
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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
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How Ernst & Young can help?
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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@nl.ey.com
Paul de Beus (Senior Manager)
Paul.de.beus@nl.ey.com
Jiajia Cui
Jiajia.cui@nl.ey.com
19
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