Investment Guarantees the new science phần 1 pps

[...]... Review of Option Pricing Theory Introduction The Guarantee Liability as a Derivative Security 95 95 96 97 98 10 0 10 1 10 1 10 2 10 4 10 8 11 2 11 5 11 5 11 6 Contents Replication and No-Arbitrage Pricing The Black-Scholes-Merton Assumptions The Black-Scholes-Merton Results The European Put Option The European Call Option Put-Call Parity Dividends Exotic Options ix 11 6 12 3 12 4 12 6 12 8 12 8 12 9 13 0 CHAPTER 8 Dynamic... 10 Emerging Cost Analysis Decisions Capital Requirements: Actuarial Risk Management Capital Requirements: Dynamic-Hedging Risk Management Emerging Costs with Solvency Capital Example: Emerging Costs for 20-Year GMAB CHAPTER 11 Forecast Uncertainty Sources of Uncertainty Random Sampling Error Variance Reduction Parameter Uncertainty Model Uncertainty 15 7 15 7 15 9 16 3 16 7 16 9 17 3 17 7 17 7 18 0 18 4 18 8 18 9... risk The insurer also sells 10 ,000 pure endowment equity-linked insurance contracts The benefit under the insurance is related to an underlying stock price index If the index value at the end of the term is greater than the starting value, then no benefit is payable If the stock price index value at the end of the contract term is less than its starting value, then the insurer must pay a benefit The probability... the contracts that offer investment guarantees as part of the benefit package We also introduce the two common methods for managing investment guarantees: the actuarial approach and the dynamic-hedging approach The actuarial approach is commonly used for risk management of investment guarantees by insurance companies in North America and in the United Kingdom The 4 INVESTMENT GUARANTEES dynamic-hedging... be the strike price of the option per unit of stock; let St be the price of one unit of the underlying stock at time t; and let T be the expiry date of the option The payoff at time T under the call option will be: (ST Ϫ K)‫ ס ם‬max(ST Ϫ K, 0) (1. 1) and the payoff under the put option will be (K Ϫ ST )‫ ס ם‬max(K Ϫ ST , 0) (1. 2) In subsequent chapters we shall see that it is natural to think of the investment. .. contingent on the policyholder’s death, and in some cases also apply to survival benefits For these contracts, the insurer’s liability at the expiry of the contract is the excess, if any, of the guaranteed minimum payout and the amount of the policyholder’s separate account Generally, the probability of the guarantee actually resulting in a benefit is small In the language of finance, we say that the guarantees. .. 11 6 12 3 12 4 12 6 12 8 12 8 12 9 13 0 CHAPTER 8 Dynamic Hedging for Separate Account Guarantees 13 3 Introduction Black-Scholes Formulae for Segregated Fund Guarantees Pricing by Deduction from the Separate Account The Unhedged Liability Examples 13 3 13 4 14 2 14 3 15 1 CHAPTER 9 Risk Measures Introduction The Quantile Risk Measure The Conditional Tail Expectation Risk Measure Quantile and CTE Measures Compared... or no investment risk for the insurer, it was natural for insurers to incorporate payment guarantees in these new contracts—this is consistent with the traditional insurance philosophy In the United Kingdom, unit-linked insurance rose in popularity in the late 19 60s through to the late 19 70s, typically combining a guaranteed minimum payment on death or maturity with a mutual fund type investment These... give the main benefit details The first three are all separate account products, and have very similar risk management and modeling issues These products form the basis of the analysis of Chapters 6 to 11 However, the techniques described in these chapters can be applied to other type of equity-linked insurance The guaranteed annuity option is discussed in Chapter 12 , and equity-indexed annuities are the. .. is the separate account and forms the major part of the benefit to the policyholder Separate account products are the source of some of the most important risk management challenges in modern insurance, and most of the examples in this book come from this class of insurance The nature of the risk to the insurer tends to be low frequency in that the stock performance must be extremely poor for the investment . 17 7 CHAPTER 11 Forecast Uncertainty 19 5 ix Contents Replication and No-Arbitrage Pricing 11 6 The Black-Scholes-Merton Assumptions 12 3 The Black-Scholes-Merton Results 12 4 The European Put Option 12 6 The. Benefit 10 0 Guaranteed Minimum Death Benefit 10 1 Example 10 1 Guaranteed Minimum Accumulation Benefit 10 2 GMAB Example 10 4 Stochastic Simulation of Liability Cash Flows 10 8 The Voluntary Reset 11 2 Introduction. index. ISBN 0-4 71- 39290 -1 (cloth : alk. paper) 1. Insurance, Life-mathematical models. 2. Risk management–Mathematical models. 1. title. II. Series. HG87 81. H 313 2003 368.32’0068 1 dc 21 2002034200 Printed