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

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

3Introduction  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: 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 (UK) £85bn / £258bn With-Profit funds have closed new business, (Interest Rate Guarantees in WP) [FSA estimates 2003]

5 Recognize Embedded Derivatives Quantity A Quantity A Quantity B Excess B-A GUARANTEE PAYS MAXIMUM OF A OR B COMPONENTS OF GUARANTEE COST

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

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

8 Valuation Methods Option Pricing Techniques TECHNIQUES TO VALUE GUARANTEES & OPTIONS ASSUMPTIONS Arbitrage Free & Complete Markets

9Replication Value of Liability Cashflows Total Value of Replicating 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;

10 Motivation & Background10  Analytic solutionsStochastic  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;

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) In each period, the insured entitles to the best or the excess return. Deficit is enlarged! Contract value Fund value

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

16 Unit-Linked Contracts 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

19Contacts Rob van Leijenhorst (AAG) Paul de Beus (Senior Manager) Jiajia Cui