金融投资是现代社会最活跃的经济活动之一。自1973年出现Black-Scholes公式以来，金融界以前所未有的速度接受数学模型和数学工具，于是出现了数学、金融、计算机和全球经济的融合。在金融数学自身的吸引力和众多使用者需求的双重影响下，美国各大学纷纷开设了相应的课程，本书正是顺应这种趋势编写的。本书主要讲解建模和对冲中使用的金融概念和数学模型。从金融方面的相关概念、术语和策略开始，逐步讨论了其中的离散模型和计算方法、以Black-Scholes公式为中心的边疆模型和解析方法，以及金融市场的风险分析及对冲策略等方面的内容。本书作为金融数学的基础教材，适用于相关专业的本科生和研究生课程。

Throughout the nineties, we have seen the synergistic union of mathematics, finance,the computer, and the global economy. Currency markets trade two trillion dollars per day, and sophisticated financial derivatives such as options, swaps. and quantos are commonplace.
　　Since the appearance of the Black-Scholes formula in l973, the financial community has embraced an abundant and ever-expanding array of mathematical tools and models. Enrollment in courses presenting these applications of mathematical finance has exploded at schools everywhere. It is driven by the attraction of the material, coupled with enormous employment demand. We expect that the twenty-first century will see even greater growth in these areas, following Kurzweil's law of accelerating returns. The practical analysis of a broad range of market transactions and activities has converted many market devotees to this mode of thinking.
　　This textbook explains the basic financial and mathematical concepts used in modeling and hedging. Each topic is introduced with the assumption that the reader has had little or no previous exposure to financial matters or to the activities that are common to major equity markets. Exercises and examples illustrate these topics.
　　Often an exercise or example uses real market data.
　　
To the Instructor
　　A complete. well-balanced course at the undergraduate level can be based on Chapters 2, 3, 5, 6. 7. 8, and 9. An instructor might touch only briefly on Chapter l as an introduction to the financial terminology and to strategies that are employed in trading equity shares. You might wish to retum to Chapter l repeatedly as you progress through the textbook; the chapter is always there as a convenient reference for market transactions and terminology.,Most undergraduate students seem to be very comfortable with computers, and they appear to pick up the ins and outs of software packages such as MapleTM, MathematicaTM, and Microsoft Excel very quickly. Each instructor will have to evaluate the proficiency of his or her own students in this area. For example, we have found that Excel is readily available on the Indiana University campus and that students are comfortable in preparing data and reports using this software.
　　
Acknowledgments
　　We would like to thank the National Science Foundation for support while preparing some of the material used in this textbook. In pariicular, we owe a great debt of gratitude to Dan Maki and Bart Ng, principal investigator on the NSF grant, "Mathematics Throughout the Curriculum," for encouraging us to write the book and for their continued support, financial and personal, during the period of creation. We wish to thank our reviewers: Rich Sowers, University of Illinois; William Yin. La Grange College; and John Chadam, University of Pittsburgh.
　　In November l999, Joseph Stampfli presented several lectures on financial mathematics at a workshop on this topic in Bangkok, Thailand, sponsored by Mahidol University. We would like to thank the university and, in particular, Professor Yongwemon Lenbury and Ponchai Matangkasombut, then Dean and now President of the university, for their gracious hospitality throughout the visit. It was a truly memorable experience.
　　We would also like to thank the editorial and production teams at Brooks/Cole for their continuous and timely help. In particular, Gary Ostedt and Carol Benedict did everything an editorial team can do and more. Several unexpected crises arose as the book progressed, and Gary guided us through them with patience. wisdom,and humor. We would also like to thank the other members of the Brooks/Cole team:Mary Vezilich, Production Coordinator; Karin Sandberg. Marketing Manager; Sue Ewing, Permissions Editor; and Samantha Cabaluna,
Marketing Communications.
　　We would also like to thank Kris Engberg of Publication Services, who helped us solve hundreds of problems, both large and small; Jerome Colburn, whose contributions as copy editor turned limp doggerel into sparkling prose; and Jason Brown and his production team.
　　Victor Goodman wishes to thank Devraj Basu for his personal input during the early stages of the manuscript preparation. In addition, Joseph Stampfli would like to
thank Jeff Gerlach, a graduate student in Economics at Indiana University. Chapter ll is entirely due to Jeff's efforts, and he provided solutions to most of the exercises.

How to Reach Us
　　Readers are encouraged to bring errors and suggestions to our attention. E-mail is excellent for this purpose. Our addresses are goodmanv@indiana.edu
　　stampfli@indiana.edu
　　A web site for this book is maintained at http://www.indiana.edu/ iubmtc/mathfinance,

Victor Goodman
Joseph Stampfli
　

1 Financial Markets
l.l Markets and Math
l.2 Stocks and Their Derivatives
l.2.l Forward Stock Contracts
l.2.2 Call Options
l.2.3 Put Options
l.2.4 Short Selling
l.3 Pricing Futures Contracts
1.4 Bond Markets
l.4.l Rates of Return
l.4.2 The U.S. Bond Market
l.4.3 Interest Rates and Forward Interest Rates
l.4.4 Yield Curves
l.5 Interest Rate Futures
l.5.l Determining the Futures Price
l.5.2 Treasury Bill Futures
l.6 Foreign Exchange
l.6.l Currency Hedging
l.6.2 Computing Currency Futures
2 Binomial Trees, Replicating Portfolios,and Arbitrage
2.l Three Ways to Price a Derivative
2.2 The Game Theory Method
2.2.l Eliminating Uncertainty
2.2.2 Valuing the Option
2.2.3 Arbitrage
2.2.4 The Game Theory Method--A General Formula
2.3 Replicating Portfolios
2.3.l The Context
2.3.2 A Portfolio Match
2.3.3 Expected Value Pricing Approach
2.3.4 How to Remember the Pricing Probability
2.4 The Probabilistic Approach
2.5 Risk
2.6 Repeated Binomial Trees and Arbitrage
2.7 Appendix: Limits of the Arbitrage Method
3 Tree Models for Stocks and Options
3.l A Stock Model
3.l.l Recombining Trees
3.l.2 Chaining and Expected Values
3.2 Pricing a Call Option with the Tree Model
3.3 Pricing an American Option
3.4 Pricing an Exotic Option--Knockout Options
3.5 Pricing an Exotic Option--Lookback Options
3.6 Adjusting the Binomial Tree Model to Real-World Data
3.7 Hedging and Pricing the N-Period Binomial Model
4 Using Spreadsheets to Compute Stock and Option Trees
4.l Some Spreadsheet Basics
4.2 Computing European Option Trees
4.3 Computing American Option Trees
4.4 Computing a Baeder Option Tree
4.5 Computing N-Step Trees
5 Continuous Models and the Black-Scholes Formula
5.l A Continuous-Time Stock Model
5.2 The Discrete Model
5.3 An Analysis of the Continuous Model
5.4 The Black-Scholes Formula
5.5 Derivation of the Black-Scholes Formula
5.5.l The Related Model
5.5.2 The Expected Value
5.5.3 Two Integrals
5.5.4 Putting the Pieces Together
5.6 Put--Call Parity
5.7 Trees and Continuous Models
5.7.l Binomial Probabilities
5.7.2 Approximation with Large Trees
5.7.3 Scaling a Tree to Match a GBM Model
5.8 The GBM Stock Price Model--A Cautionary Tale
5.9 Appendix: Construction of a Brownian Path
6 The Analytic Approach to Black-Scholes
6.l Strategy for Obtaining the Differential Equation
6.2 Expanding V(S,t)
6.3 Expanding and Simplifying V(St, t)
6.4 Finding a Portfolio
6.5 Solving the Black-Scholes Differential Equation
6.5.l Cash or Nothing Option
6.5.2 Stock--or-Nothing Option
6.5.3 European Call
6.6 Options on Futures
6.6.l Call on a Futures Contract
6.6.2 A PDE for Options on Futures
6.7 Appendix: Portfolio Differentials
7 Hedging
7.l Delta Hedging
7.l.l Hedging, Dynamic Programming, and a Proof that
Black--Scholes Really Works in an Idealized World
7.l.2 Why the Foregoing Argument Does Not Hold in the Real World
7.l.3 Earlier A Hedges
7.2 Methods for Hedging a Stock or Portfolio
7.2.l Hedging with Puts
7.2.2 Hedging with Collars
7.2.3 Hedging with Paired Trades
7.2.4 Correlation-Based Hedges
7.2.5 Hedging in the Real World
7.3 Implied VOlatiIity
7.3.l Computing　with Maple
7.3.2 The Volatility Smile
7.4 The Parameters A, r, and O
7.4.l The Ro1e of r
7.4.2 A Further Role for A, r, O
7.5 Derivation of the Delta Hedging Rule
7.6 DeIta Hedging a Stock PUrchase
8 Bond Models and Interest Rate Options
8.l Interest Rates and Forward Rates
8.l.1 Size
8.l.2 The Yield Curve
8.l.3 How Is the vield Curve Determined
8.l.4 Forward Rates
8.2 Zero-Coupon Bonds
8.2.l Forward Rates and ZCBs
8.2.2 Computations Based on Y(t) or P(t)
8.3 Swaps
8.3.l Another Variation on Payments
8.3.2 A More Realistic Scenario
8.3.3 Models for Bond Prices
8.3.4 Arbitrage
8.4 Pricing and Hedging a Swap
8.4.l Arithmetic Interest Rates
8.4.2 Geometric Interest Rates
8.5 Interest Rate Models
8.5.l Discrete Interest Rate Models
8.5.2 Pricing ZCBs from the Interest Rate Model
8.5.3 The Bond Price Paradox
8.5.4 Can the Expected Value Pricing Method Be Hrbitraged
8.5.5 Continuous Models
8.5.6 A Bond Price Model
8.5.7 A Simple Example
8.5.8 The Vasicek Model
8.6 Bond Price Dynamics
8.7 A Bond Price Formula
8.8 Bond Prices, Spot Rates, and HJM
8.8.1 Example: The Hall-White Model
8.9 The Derivative Approach to HJM: The HJM Miracle
8.lO Appendix: Forward Rate Drift
9 Computational Methods for Bonds
9.l Tree Models for Bond Prices
9.l.1 Fair and Unfair Games
9.l.2 The Ho-Lee Model
9.2 A Binomial Vasicek Model: A Mean Reversion Model
9.2.l The Base Case
9.2.2 The General Induction Step
10 Currency Markets and Foreign Exchange Risks
1O.l The Mechanics of Trading
lO.2 Currency Forwards: Interest Rate Parity
1O.3 Foreign Currency Options
lO.3.l The Garrnan-Kohlhagen Formula
lO.3.2 Put--Call Parity for Currency Options
lO.4 Guaranteed Exchange Rates and Quantos
lO.4.l The Bond Hedge
lO.4.2 Pricing the GER Forward on a Stock
lO.4.3 Pricing the GER Put or Call Option
1O.5 To Hedge or Not to Hedgeand How Much
11 International Political Risk Analysis
ll.1 Introduction
ll.2 Types of International Risks
ll.2.l Political Risk
ll.2.2 Managing International Risk
1l.2.3 Diversification
ll.2.4 Political Risk and Export Credit Insurance
ll.3 Credit Derivatives and the Management of Political Risk
ll.3.l Foreign Currency and Derivatives
ll.3.2 Credit Default Risk and Derivatives
1l.4 Pricing International Political Risk
l1.4.l The Credit Spread or Risk Premium on Bonds
ll.5 Two Models for Determining the Risk Premium
ll.5.1 The Black--Scholes Approach to Pricing Risky Debt
ll.5.2 An Alternative Approach to Pricing Risky Debt
ll.6 A Hypothetical Example of the JLT Model
Answers to Selected Exercises
Index