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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

2

4

6

8

10

12

14

16

18

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

2

3

4

5

6

7

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)Rob.van.leijenhorst@nl.ey.com

Paul de Beus (Senior Manager)Paul.de.beus@nl.ey.com

Jiajia CuiJiajia.cui@nl.ey.com