金融模型中的鞅方法 ：第2版

Preface to the Second Edition

Note on the Second Printing

Preface to the First Edition

Part 1 Spot and Futures Markets

1 An Introduction to Financial Derivatives

1.1 Options

1.2 Futures Contracts and Options

1.3 Forward Contracts

1.4 CallandPutSpotOptions

1.4.1 One-period Spot Market

1.4.2 Replicating Portfolios

1.4.3 Martingale Measure for a Spot Market

1.4.4 Absence of Arbitrage

1.4.5 Optimality of Replication

1.4.6 Change of a Numeraire

1.4.7 Put Option

1.5 Forward Contracts

1.5.1 Forward Price

1.6 Futures Call and Put Options

1.6.1 Futures Contracts and Futures Prices

1.6.2 One-period Futures Market

1.6.3 Martingale Measure for a Futures Market

1.6.4 Absence of Arbitrage

1.6.5 One-period Spot/Futures Market

1.7 Options of American Style

1.8 Universal No-arbitrage Inequalities

2 Discrete-time Security Markets

2.1 The Cox-Ross-Rubinstein Model

2.1.1 Binomial Lattice for the Stock Price

2.1.2 Recursive Pricing Procedure

2.1.3 CRR Option Pricing Formula

2.2 Martingale Properties of the CRR Model

2.2.1 Martingale Measures

2.2.2 Risk-neutral Valuation Formula

2.2.3 Change of a Numeraire

2.3 The Black-Scholes Option Pricing Formula

2.4 Valuation of American Options

2.4.1 American Call Options

2.4.2 American Put Options

2.4.3 American Claims..

2.5 Options on a Dividend-paying Stock

2.6 Security Markets in Discrete Time

2.6.1 Finite Spot Markets..

2.6.2 Self-financing Trading Strategies

2.6.3 Replication and Arbitrage Opportunities

2.6.4 Arbitfage Price

2.6.5 Risk-neutral Valuation Formula

2.6.6 Existence of a Martingale Measure

2.6.7 Completeness of a Finite Market

2.6.8 Separating Hyperplane Theorem

2.6.9 Change of a Numeraire

2.6.10 Discrete-time Models with Infinite State Space

2.7 Finite Futures Markets

2.7.1 Self-financing Futures Strategies

2.7.2 Martingale Measures for a Futures Market

2.7.3 Risk-neutral Valuation Formula

2.7.4 Futures Prices Versus Forward Prices

2.8 American Contingent Claims

2.8.1 Optimal Stopping Problems

2.8.2 Valuation and Hedging of American Claims

2.8.3 American Call and Put

2.9 Game Contingent Claims

2.9.1 Dynkin Games

2.9.2 Valuation and Hedging of Game Contingent Claims

3 Benchmark Models in Continuous Time

3.1 The Black-Scholes Model

3.1.1 Risk-free Bond

3.1.2 Stock Price

3.1.3 Self-financing Trading Strategies

3.1.4 Martingale Measure for the Black-Scholes Model

……

Part II Fixed-income Markets

Part III APPENDIX

References

Index

Let us stress that we have only taken out few sections that， in our opinion， were of marginal importance for the understanding of the fundamental principles of financial modelling of arbitrage valuation of derivatives. In view of the abundance of new results in the area， it would be in any case unimaginable to cover all existing approaches to pricing and hedging financial derivatives （not to mention allimportantresults） in a single book， no matter how voluminous it were. Hence， several intensively studied areas， such as: mean-variance hedging， utility-based pricing， entropybased approach， financial models with frictions （e.g.， short-selling constraints， bidask spreads， transaction costs， etc.） either remain unmentioned in this text， or are presented very succinctly. Although the issue of market incompleteness is not totally neglected，it is examined primarily in the framework of models of stochastic （oruncertain） volatility. Luckily enough， the afore-mentioned approaches and results are covered exhaustively in several excellent monographs written in recent years by our distinguished colleagues， and thus it is our pleasure to be able to refer the interested reader to these texts.