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Embedded Options and Guarantees

Embedded Options and Guarantees. Rob van Leijenhorst (AAG), Jiajia Cui AFIR2003 colloquium, Sep. 19th. 2003. Agenda. Introduction Importance of Guarantees Recognizing Guarantees and the Embedded Options Valuation Methods Case Studies How to Win the Chess Game. Introduction.

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Embedded Options and Guarantees

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  1. Embedded Options and Guarantees Rob van Leijenhorst (AAG), Jiajia Cui AFIR2003 colloquium, Sep. 19th. 2003

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

  3. 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

  4. 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]

  5. Recognize Embedded Derivatives GUARANTEE PAYS MAXIMUM OF A OR B COMPONENTS OF GUARANTEE COST Q u a n t i t y E x c e s s B - A B Q u a n t i t y Q u a n t i t y A A

  6. Examples SAMPLE CONTRACT QUANTITY A QUANTITY B Sum assured plus vested bonuses Asset Share UK Traditional participating insurance with guaranteed sums assured and reversionary bonuses Premium accumulated at the guaranteed rate over the term of the contract Account Balance NL Unit-Linked contract with a maximum of maturity benefit or return of premium accumulated at a guaranteed minimum crediting rate Funds required to purchase the guaranteed annuity using current terms Account Balance US Guaranteed Minimum Income Benefit (similar to Guaranteed Annuity Option in the UK)

  7. Fair Value Accounting 3% 2% 14% Fair Value/Option Pricing Only When In-The-Money 6% Not Explicitly Not At All Other 76%

  8. Valuation Methods TECHNIQUES TO VALUE GUARANTEES & OPTIONS O p t i o n P r i c i n g T e c h n i q u e s ASSUMPTIONS Arbitrage Free & Complete Markets

  9. Replication L i a b i l i t y C a s h f l o w s • Pros: Perfect Replication; Hedging + Valuation • Cons: limited to few cases;limited by available financial instruments; G u a r a n t e e C o s t s N o r m a l B e n e f i t s 1 2 3 4 5 T I M E R e p l i c a t i n g A s s e t f o r N o r m a l B e n e f i t s 1 2 3 4 5 T I M E R e p l i c a t i n g A s s e t f o r G u a r a n t e e C o s t s T I M E 1 2 3 4 5 V a l u e o f T o t a l V a l u e o f L i a b i l i t y R e p l i c a t i n g C a s h f l o w s A s s e t s

  10. 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; Motivation & Background

  11. 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

  12. 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

  13. 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.

  14. 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 insuredentitles to the best of @4% or the excess return. Deficit is enlarged!

  15. Case Study (2): With-Profit Contracts (cont.) • Deficit compensation • Conditional Profit-sharing Contract value In each period, if no deficit, the insuredentitles to the best of @4% or the excess return. deficit Deficit is limited!

  16. Numerical Results (1): Unit-Linked Contracts • As % of PV premiums • Single premium v.s. regular premium

  17. Numerical Results (2): With-Profit contracts • As % of PV premiums • Annual profit-sharing v.s. conditional profit-sharing

  18. 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

  19. 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

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