本书由剑桥大学出版社出版，原书名为：Financial Engineering and Computation: Principles, Mathematics, and Algorithms，是一本非常优秀的有关金融计算的图书。

如今打算在金融领域工作的学生和专家不仅要掌握先进的概念和数学模型，还要学会如何在计算上实现这些模型。本书内容广泛，不仅介绍了金融工程背后的理论和数学，并把重点放在了计算上，以便和金融工程在今天资本市场的实际运作保持一致。本书不同于大多数的有关投资、金融工程或者衍生证券方面的书，而是从金融的基本想法开始，逐步建立理论。作者提供了很多定价、风险评估以及项目组合管理的算法和理论。本书的重点是有关金融产品和衍生证券、期权、期货、远期、利率衍生产品、抵押证券等等的定价问题。每个工具都有简要的介绍，每章都可以独立被引用。本书的算法均使用Java算法编程实现的，并可以在相关的网站上下载。

本书可供金融MBA、金融学和金融工程方向的学生、计算金融的研究人员以及金融分析师参考使用。

过去十年来，许多复杂的数学和计算技巧为分析金融市场而发展起来。有意在任何金融领域工作的学生和业界人士不仅必须掌握高级的概念和数学模型，并且还必须学会怎样在计算上实现这些模型。本书全面讨论了金融工程背后的理论和数学，并强调了在当今资本市场中金融工程实际应用的计算。

与大多数有关投资学、金融工程或衍生证券的书不同的是，本书从金融学的基本观念出发，逐步构建理论。在现代金融学中所需要的高级数学概念以一种可接受的层次来阐释。这样，它就为金融方面的MBA、有志于从事金融业的理工科学生、计算金融的研究工作者、系统分析师和金融工程师在这一主题上提供了全面的基础。

构建理论的同时，作者介绍了在定价、风险管理和证券组合管理方面的计算技巧的算法，并且对它们的效率进行了分析。对金融证券和衍生证券的定价是本书的中心论题。各种各样的金融工具都得到讨论：债券、期权、期货、远期、利率衍生品、有抵押支持的证券、嵌入期权的债券，以及诸如此类的其他工具。为便于参考使用，每种金融工具都以简短而自成体系的一章来论述。

Preface

Useful Abbreviations

1 Introduction

1.1 Modern Finance: A Brief History

1.2 Financial Engineering and Computation

1.3 Financial Markets

1.4 Computer Technology

2 Analysis of Algorithms

2.1 Complexity

2.2 Analysis of Algorithms

2.3 Description of Algorithms

2.4 Software Implementation

3 Basic Financial Mathematics

3.1 Time Value of Money

3.2 Annuities

3.3 Amortization

3.4 Yields

3.5 Bonds

4 Bond Price Volatility

4.1 Price Volatility

4.2 Duration

4.3 Convexity

5 Term Structure of Interest Rates

5.1 Introduction

5.2 Spot Rates

5.3 Extracting Spot Rates from Yield Curves

5.4 Static Spread

5.5 Spot Rate Curve and Yield Curve

5.6 Forward Rates

5.7 Term Structure Theories

5.8 Duration and Immunization Revisited

6 Fundamental Statistical Concepts

6.1 Basics

6.2 Regression

6.3 Correlation

6.4 Parameter Estimation

7 Option Basics

7.1 Introduction

7.2 Basics

7.3 Exchange-Traded Options

7.4 Basic Option Strategies

8 Arbitrage in Option Pricing

8.1 The Arbitrage Argument

8.2 Relative Option Prices

8.3 Put-Call Parity and Its Consequences

8.4 Early Exercise of American Options

8.5 Convexity of Option Prices

8.6 The Option Portfolio Property

9 Option Pricing Models

9.1 Introduction

9.2 The Binomial Option Pricing Model

9.3 The Black-Scholes Formula

9.4 Using the Black-Scholes Formula

9.5 American Puts on a Non-Dividend-Paying Stock

9.6 Options on a Stock that Pays Dividends

9.7 Traversing the Tree Diagonally

10 Sensitivity Analysis of Options

10.1 Sensitivity Measures ("The Greeks")

10.2 Numerical Techniques

11 Extensions of Options Theory

11.1 Corporate Securities

11.2 Barrier Options

11.3 Interest Rate Caps and Floors

11.4 Stock Index Options

11.5 Foreign Exchange Options

11.6 Compound Options

11.7 Path-Dependent Derivatives

12 Forwards, Futures, Futures Options, Swaps

12.1 Introduction

12.2 Forward Contracts

12.3 Futures Contracts

12.4 Futures Options and Forward Options

12.5 Swaps

13 Stochastic Processes and Brownian Motion

13.1 Stochastic Processes

13.2 Martingales ("Fair Games")

13.3 Brownian Motion

13,4 Brownian Bridge

14 Continuous-Time Financial Mathematics

14.1 Stochastic Integrals

14.2 Ito Processes

14.3 Applications

14.4 Financial Applications

15 Continuous-Time Derivatives Pricing

15.1 Partial Differential Equations

15.2 The Black-Schotes Differential Equation

15.3 Applications

15.4 General Derivatives Pricing

15.5 Stochastic Volatility

16 Hedging

16.1 Introduction

16.2 Hedging and Futures

16.3 Hedging and Options

17 Trees

17.1 Pricing Barrier Options with Combinatorial Methods

17.2 Trinomial Tree Algorithms

17.3 Pricing Multivariate Contingent Claims

18 Numerical Methods

18.1 Finite-Difference Methods

18.2 Monte Carlo Simulation

18.3 Quasi-Monte Carlo Methods

19 Matrix Computation

19.1 Fundamental Definitions and Results

19.2 Least-Squares Problems

19.3 Curve Fitting with Splines

20 Time Series Analysis

20.1 Introduction

20.2 Conditional Variance Models for Price Volatility

21 Interest Rate Derivative Securities

21.1 Interest Rate Futures and Forwards

21.2 Fixed-Income Options and Interest Rate Options

21.3 Options on Interest Rate Futures

21.4 Interest Rate Swaps

22 Term Structure Fitting

22.1 Introduction

22.2 Linear Interpolation

22.3 Ordinary Least Squares

22.4 Splines

22.5 The Nelson-Siegel Scheme

23 Introduction to Term Structure Modeling

23.1 Introduction

23.2 The Binomial Interest Rate Tree

23.3 Applications in Pricing and Hedging

23.4 Volatility Term Structures

24 Foundations of Term Structure Modeling

24.1 Terminology

24.2 Basic Relations

24.3 Risk-Neutral Pricing

24.4 The Term Structure Equation

24.5 Forward-Rate Process

24.6 The Binomial Model with Applications

24.7 Black-Scholes Models

25 Equilibrium Term Structure Models

25.1 The Vasicek Model

25.2 The Cox-Ingersoll-Ross Model

25.3 Miscellaneous Models

25.4 Model Calibration

25.5 One-Factor Short Rate Models

26 No-Arbitrage Term Structure Models

26.1 Introduction

26.2 The Ho-Lee Model

26.3 The Black-Derman-Toy Model

26.4 The Models According to Hull and White

26.5 The Heath-Jarrow-Morton Model

26.6 The Ritchken-Sankarasubramanian Model

27 Fixed-Income Securities

27.1 Introduction

27.2 Treasury, Agency, and Municipal Bonds

27.3 Corporate Bonds

27.4 Valuation Methodologies

27.5 Key Rate Durations

28 Introduction to Mortgage-Backed Securities

28.1 Introduction

28.2 Mortgage Banking

28.3 Agencies and Securitization

28.4 Mortgage-Backed Securities

28.5 Federal Agency Mortgage-Backed Securities Programs

28.6 Prepayments

29 Analysis of Mortgage-Backed Securities

29.1 Cash Flow Analysis

29.2 Collateral Prepayment Modeling

29.3 Duration and Convexity

29.4 Valuation Methodologies

30 Collateralized Mortgage Obligations

30.1 Introduction

30.2 Floating-Rate Tranches

30.3 PAC Bonds

30.4 TAC Bonds

30.5 CMO Strips

30.6 Residuals

31 Modern Portfolio Theory

31.1 Mean-Variance Analysis of Risk and Return

31.2 The Capital Asset Pricing Model

31.3 Factor Models

31.4 Value at Risk

32 Software

32.1 Web Programming

32.2 Use of The Capitals Software

32.3 Further Topics

33 Answers to Selected Exercises

Bibliography

Glossary of Useful Notations

Index