Embedded Options and Guarantees
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Transcript of Embedded Options and Guarantees
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Embedded Options and Guarantees
Embedded Options and GuaranteesEmbedded Options and Guarantees
Rob van Leijenhorst (AAG), Jiajia Cui
AFIR2003 colloquium, Sep. 19th. 2003
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AgendaAgenda
Introduction Importance of Guarantees Recognizing Guarantees and the Embedded Options Valuation Methods Case Studies How to Win the Chess Game
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IntroductionIntroduction
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 MatterGuarantees Matter
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
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 DerivativesRecognize Embedded Derivatives
QuantityA
QuantityA
QuantityB
Excess B-A
GUARANTEE PAYSMAXIMUM OF A OR B
COMPONENTS OFGUARANTEE COST
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ExamplesExamples
SAMPLE CONTRACT
UK Traditional participatinginsurance with guaranteedsums assured andreversionary bonuses
NL Unit-Linked contract with a maximum of maturity benefit or return of premium accumulated
at a guaranteed minimumcrediting rate
US Guaranteed MinimumIncome Benefit (similar toGuaranteed Annuity Optionin the UK)
QUANTITY A
Asset Share
Account Balance
Account Balance
Sum assured plus vestedbonuses
Premium accumulated atthe guaranteed rate overthe term of the contract
Funds required to purchasethe guaranteed annuityusing current terms
QUANTITY B
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Fair Value AccountingFair Value Accounting
Fair Value/Option Pricing
Only When In-The-Money
Not Explicitly
Not At All
Other76%
6%
14%
2% 3%
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Valuation MethodsValuation Methods
O p t i o nP r i c i n g
T e c h n i q u e s
TECHNIQUES TO VALUEGUARANTEES & OPTIONS
ASSUMPTIONSArbitrage Free & Complete Markets
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ReplicationReplication
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Value ofLiability
Cashflows
Total Value ofReplicating
Assets
Liability Cashflows
TIME
TIME
TIME
Replicating Asset for Normal Benefits
Replicating Asset for Guarantee Costs
Guarantee Costs
Normal Benefits
Pros: Perfect Replication; Hedging + Valuation
Cons: limited to few cases; limited by available financial instruments;
Motivation & Background 10!@#10
Analytic solutions
StochasticStochastic
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 Case studies byby Simulations 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 studiesCase 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 StudyCase Study (1): Unit-Linked Contracts (1): Unit-Linked Contracts
Minimum Rate of Return Guarantee (e.g. 4% per year)
Maturity Profit-sharing
0 20 40 60 80 100 120 1400
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4
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10
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20regular premium Unit-Linked contract (2 scenarios)
contract maturity (months)
shortfall
profit
The insured entitles to the best of either the full fund value or a guaranteed minimum amount at maturity.
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Case StudyCase Study (2): (2): With-Profit Contracts With-Profit Contracts
Annual Profit-sharing (e.g. the excess return over 4% is added to the sum assured)
Distribution ratio (80%), margin (50bp)
In each period, the insured entitles to the best of @4% or the excess return.
Deficit is enlarged! 0 5 10 15 20 25 301
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stock fundcontract
single premium With-Profit Contract (80% distribution ratio, no deficit compensation) (on stock)
contract maturity
Contract value
Fund value
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Case StudyCase Study (2): (2): With-Profit Contracts With-Profit Contracts (cont.) (cont.)
0 5 10 15 20 25 300
5
10
15
20
25single premium annual guarantee with deficit deduction and profit-sharing (on stock)
deficitcontract
Deficit compensation Conditional Profit-
sharing
Contract value
deficit
Deficit is limited!
In each period, if no deficit, the insured entitles to the best of @4% or the excess return.
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Numerical Results (1): Unit-Linked Contracts Unit-Linked Contracts
As % of PV premiums Single premium v.s. regular premium
(UL) maturity guarantee on Stock
0
0,05
0,1
0,15
0,2
0 10 20 30 40
contract maturity
IRG single prem
regular prem
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Numerical Results (2): With-Profit contracts
(WP) yearly premium annual guarantee on Mix Fund (80%B 20%S)
0
0,1
0,2
0,3
0,4
0,5
0 10 20 30 40
buffer(80%dis)margin(25bp)
deficitcompensation
As % of PV premiums Annual profit-sharing v.s. conditional profit-sharing
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How to Win the Chess GameHow 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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ContactsContacts
Rob van Leijenhorst (AAG)[email protected]
Paul de Beus (Senior Manager)[email protected]
Jiajia [email protected]