本书旨在讲述研究现代金融市场衍生证券，如期权、期货和交换业务等所需的数学知识。建立在著名的Black-Scholes理论基础上的理想化连续时间模型需要对现代微积分有较深的了解。然而，书中许多潜在的知识点完全可以在离散时间的框架内理解。本书是在第1版的基础上做了较多增补，使得连续时间理论应用范围更加广泛，更加详细地介绍Black-Scholes模型及其推广、期限结构和消费投资问题。增加的内容有：一致性风险测度及其在对冲中的应用；一般离散市场模型中资产估价的第一基本定理；不完全离散市场的套利区间；完全离散市场的特征；Black-Scholes模型中的风险、回报和灵敏度。

Preface

Preface to the Second Edition

1 Prlcing by Arbitrage

 1.1 Introduction: Pricing and Hedging

 1.2 Single-Period Option Pricing Models

 1.3 A General Single-Period Model

 1.4 A Single-Period Binomial Model

 1.5 Multi-period Binomial Models

 1.6 Bounds on Option Prices

2 Martingale Measures

 2.1 A General Discrete-Time Market Model

 2.2 Trading Strategies

 2.3 Martingales and Risk-Neutral Pricing

 2.4 Arbitrage Pricing: Martingale Measures

 2.5 Strategies Using Contingent Claims

 2.6 Example: The Binomial Model

 2.7 From CRR to Blaek-Scholes

3 The First Fundamental Theorem

 3.1 The Separating Hyperplane Theorem in Rn

 3.2 Construction of Martingale Measures

 3.3 Pathwise Description

 3.4 Examples

 3.5 General Discrete Models

4 Complete Markets

 4.1 Completeness and Martingale Representation

 4.2 Completeness for Finite Market Models

 4.3 The CRR Model

 4.4 The Splitting Index and Completeness

 4.5 Incomplete Models: The Arbitrage Interval

 4.6 Characterisation of Complete Models

5 Discrete-time American Options

 5.1 Hedging American Claims

 5.2 Stopping Times and Stopped Processes

 5.3 Uniformly Integrable Martingales

 5.4 Optimal Stopping: The Snell Envelope

 5.5 Pricing and Hedging American Options

 5.6 Consumption-Investment Strategies

6 Continuous-Time Stochastic Calculus

 6.1 Continuous-Time Processes

 6.2 Martingales

 6.3 Stochastic Integrals

 6.4 The It8 Calculus

 6.5 Stochastic Differential Equations

 6.6 Markov Property of Solutions of SDEs

7 Continuous-Time European Options

 7.1 Dynamics

 7.2 Girsanov's Theorem

 7.3 Martingale Representation

 7.4 Self-Financing Strategies

 7.5 An Equivalent Martingale Measure

 7.6 Black-Scholes Prices

 7.7 Pricing in a Multifactor Model

 7.8 Barrier Options

 7.9 The Black-Scholes Equation

 7.10 The Greeks

8 The American Put Option

 8.1 Extended Trading Strategies

 8.2 Analysis of American Put Options

 8.3 The Perpetual Put Option

 8.4 Early Exercise Premium

 8.5 Relation to Free Boundary Problems

 8.6 An Approximate Solution

9 Bonds and Term Structure

 9.1 Market Dynamics

 9.2 Future Price and Futures Contracts

 9.3 Changing Numeraire

 9.4 A General Option Pricing Formula

 9.5 Term Structure Models

 9.6 Short-rate Diffusion Models

 9.7 The Heath-Jarrow-Morton Model

 9.8 A Markov Chain Model

10 Consumption-Investment Strategies

 10.1 Utility Functions

 10.2 Admissible Strategies

 10.3 Maximising Utility of Consumption

 10.4 Maximisation of Terminal Utility

 10.5 Consumption and Terminal Wealth

11 Measures of Risk

 11.1 Value at Risk

 11.2 Coherent Risk Measures

 11.3 Deviation Measures

 11.4 Hedging Strategies with Shortfall Risk

Bibliography

Index