Embedded Options and Guarantees Embedded Options and Guarantees

Embedded Options and Guarantees !@# Embedded Options and Guarantees Rob van Leijenhorst (AAG), Jiajia Cui AFIR 2003 colloquium, Sep. 19 th. 2003

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

Introduction Traditional actuarial valuations / profit testing ¢ Guarantees are not explicitly priced ¢ No extra reserve for guarantees Markets meltdown ¢ ¢ Ernst & Young investigations on Guarantee issues ¢ ¢ 3 Low interest rates Bearish equity markets Global Netherlands !@#

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 ¢ ¢ ¢ 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) £ 85 bn / £ 258 bn With-Profit funds have closed new business, (Interest Rate Guarantees in WP) [FSA estimates 2003] !@#

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

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 !@#

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

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 !@#

Replication Liability Cashflows Guarantee Costs Normal Benefits 1 2 3 TIME Replicating Asset for Normal Benefits 4 5 TIME 1 2 3 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 !@#

Stochastic Analytic solutions 10 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 !@# 10

Case studies by Simulations Why simulation? ¢ Existing products ¢ ¢ ¢ 11 Complex cash flows, multi-assets Unit-Linked products With-Profit products Group pension contracts Existing investment strategies !@#

Case studies Contract conditions + investment strategies determine the characteristics & values of guarantees Stochastic Assets modelling ¢ ¢ 12 The Correlated Black-Scholes & Hull White Model Money market account, Stock account, Bond portfolio, Mix fund !@#

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. 13 !@#

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 (50 bp) Contract value Fund value In each period, the insured entitles to the best of @4% or the excess return. Deficit is enlarged! 14 !@#

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

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

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

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? ¿ ¿ ¿ 18 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 !@#

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 !@#