1 INTRODUCTION

1．1 Forward Contracts

1 INTRODUCTION

1．2 Futures Contracts

1．3 Options

1．4 Other Derivatives

1．5 Types of Traders

Questions and Problems

1．6 Summary

2．1 Trading Futures Contracts

2 FUTURES MARKETS AND THE USE OF FUTURES FOR HEDGING

2 FUTURES MARKETS AND THE USE OF FUTURES FOR HEDGING

2．2 Specification of the Futures Contract

2．3 Operation of Margins

2．4 Newspaper Quotes

2．5 Convergence of Futures Price to Spot Price

2．6 Settlement

2．7 Regulation

2．8 Hedging Using Futures

2．9 Optimal Hedge Ratio

2．10 Rolling the Hedge Forward

2．11 Accounting and Tax

2．12 Summary

Suggestions for Further Reading

Questions and Problems

3 FORWARD AND FUTURES PRICES

3．1 Some Preliminaries

3 FORWARD AND FUTURES PRICES

3．2 Forward Contracts on a Security That Provides No Income

3．3 Forward Contracts on a Security That Provides a Known Cash Income

3．4 Forward Contracts on a Security That Provides a Known Dividend Yield

3．6 Forward Prices versus Futures Prices

3．5 General Result

3．7 Stock Index Futures

3．8 Forward and Futures Contracts on Currencies

3．9 Futures on Commodities

3．10 The Cost of Carry

3．11 Delivery Choices

3．12 Futures Prices and the Expected Future Spot Price

3．13 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 3A Proof That Forward and Futures Prices Are Equal When Interest Rates Are Constant

4 INTEREST RATE FUTURES

4．1 Some Preliminaries

4 INTEREST RATE FUTURES

4．2 Forward Rate Agreements

4．3 Treasury Bond and Treasury Note Futures

4．4 Treasury Bill Futures

4．5 Eurodollar Futures

4．6 Duration

4．7 Duration-Based Hedging Strategies

4．8 Limitations of Duration

4．9 Summary

Suggestions for Further Reading

Questions and Problems

5 SWAPS

5．1 Mechanics of Interest Rate Swaps

5 SWAPS

5．2 The Comparative Advantage Argument

5．3 Valuation of Interest Rate Swaps

5．4 Currency Swaps

5．5 Valuation of Currency Swaps

5．6 Other Swaps

5．7 Credit Risk

5．8 Summary

Suggestions for Further Reading

Questions and Problems

6 OPTIONS MARKETS

6．1 Exchange-Traded Options

6 OPTIONS MARKETS

6．2 Over-the-Counter Options

6．3 Specification of Stock Options

6．4 Newspaper Quotes

6．5 Trading

6．6 Commissions

6．7 Margins

6．8 The Options Clearing Corporation

6．9 Regulation

6．10 Taxation

6．11 Warrants and Convertibles

6．12 Summary

Suggestions for Further Reading

Questions and Problems

7 PROPERTIES OF STOCK OPTION PRICES

7．1 Factors Affecting Option Prices

7 PROPERTIES OF STOCK OPTION PRICES

7．2 Assumptions and Notation

7．3 Upper and Lower Bounds for Option Prices

7．4 Early Exercise：Calls on a Non-Dividend-Paying Stock

7．5 Early Exercise：Puts on a Non-Dividend-Paying Stock

7．6 Put-Call Parity

7．7 Effect of Dividends

7．8 Empirical Research

7．9 Summary

Suggestions for Further Reading

Questions and Problems

8 TRADING STRATEGIES INVOLVING OPTIONS

8．1 Strategies Involving a Single Option and a Stock

8 TRADING STRATEGIES INVOLVING OPTIONS

8．2 Spreads

8．3 Combinations

8．4 Other Payoffs

8．5 Summary

Suggestions for Further Reading

Questions and Problems

9 INTRODUCTION TO BINOMIAL TREES

9．1 One-Step Binomial Model

9 INTRODUCTION TO BINOMIAL TREES

9．2 Risk-Neutral Valuation

9．3 Two-Step Binomial Trees

9．4 Put Example

9．5 American Options

9．6 Delta

9．7 Using Binomial Trees in Practice

9．8 Summary

Suggestions for Further Reading

Questions and Problems

10 MODEL OF THE BEHAVIOR OF STOCK PRICES

10．1 The Markov Property

10 MODEL OF THE BEHAVIOR OF STOCK PRICES

10．2 Wiener Processes

10．3 The Process for Stock Prices

10．4 Review of the Model

10．5 The Parameters

10．6 Ito s Lemma

10．7 Summary

Questions and Problems

Suggestions for Further Reading

Appendix 10A Derivation of Ito s Lemma

11 THE BLACK-SCHOLES ANALYSIS

11．1 Lognormal Property of Stock Prices

11 THE BLACK-SCHOLES ANALYSIS

11．2 The Distribution of the Rate of Return

11．3 Estimating Volatility form Historical Data

11．4 Concepts Underlying the Black-Scholes Differential Equation

11．5 Derivation of the Black-Scholes Differential Equation

11．6 Risk-Neutral Valuation

11．7 Black-Scholes Pricing Formulas

11．8 Cumulative Normal Distribution Function

11．9 Warrants Issued by a Company on Its Own Stock

11．10 Implied Volatilities

11．11 The Causes of Volatility

11．12 Dividends

11．13 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 11A Exact Procedure for Calculating Values of American Calls on Dividend-Paying Stocks

Appendix 11B Calculation of Cumulative Probability in Bivariate Normal Distribution

12 OPTIONS ON STOCK INDICES， CURRENCIES， AND FUTURES CONTRACTS

12 OPTIONS ON STOCK INDICES， CURRENCIES， AND FUTURES CONTRACTS

12．1 Extending Black-Scholes

12．2 Pricing Formulas

12．3 Options on Stock Indices

12．4 Currency Options

12．5 Futures Options

12．6 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 12A Derivation of Differential Equation Satisfied by a Derivative Dependent on a Stock Paying a Continuous Dividend Yield

Appendix 12B Derivation of Differential Equation Satisfied by a Derivative Dependent on a Futures Price

13 GENERAL APPROACH TO PRICING DERIVATIVES

13 GENERAL APPROACH TO PRICING DERIVATIVES

13．1 Single Underlying Variable

13．2 Interest Rate Risk

13．3 Securities Dependent on Several State Variables

13．4 Is It Necessary to Estimate the Market Price of Risk？

13．5 Derivatives Dependent on Commodity Prices

13．6 Quantos

13．7 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 13A Generalization of Ito s Lemma

Appendix 13B Derivation of the General Differential Equation Satisfied by Derivatives

14 THE MANAGEMENT OF MARKET RISK

14．1 Example

14 THE MANAGEMENT OF MARKET RISK

14．2 Naked and Covered Positions

14．3 A Stop-Loss Strategy

14．4 More Sophisticated Hedging Schemes

14．5 Delta Hedging

14．6 Theta

14．7 Gamma

14．8 Relationship among Delta， Theta， and Gamma

14．9 Vega

14．10 Rho

14．11 Scenario Analysis

14．12 Portfolio Insurance

14．13 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 14A Taylor Series Expansions and Hedge Parameters

15 NUMERICAL PROCEDURES

15．1 Binomial Trees

15 NUMERICAL PROCEDURES

15．2 Using the Binomial Tree for Options on Indices， Currencies， and Futures Contracts

15．3 Binomial Model for a Dividend-Paying Stock

15．4 Extensions of the Basic Tree Approach

15．5 Alternative Procedures for Constructing Trees

15．6 Monte Carlo Simulation

15．7 Variance Reduction Procedures

15．8 Finite Difference Methods

15．9 Analytic Approximations in Option Pricing

15．10 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 15A Analytic Approximation to American Option Prices of Macmillan， and Barone-Adesi and Whaley

16 INTEREST RATE DERIVATIVES AND THE USE OF BLACK S MODEL

16．1 Exchange-Traded Interest Rate Options

16 INTEREST RATE DERIVATIVES AND THE USE OF BLACK S MODEL

16．2 Embedded Bond Options

16．3 Mortgage-Backed Securities

16．4 Option-Adjusted Spread

16．5 Black s Model

16．6 European Bond Options

16．7 Interest Rate Caps

16．8 European Swap Options

16．9 Accrual Swaps

16．10 Spread Options

16．11 Convexity Adjustments

16．12 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 16A Proof of the Convexity Adjustment Formula

17 INTEREST RATE DERIVATIVES AND MODELS OF THE YIELD CURVE

17．1 Introduction to Equilibrium Models

17 INTEREST RATE DERIVATIVES AND MODELS OF THE YIELD CURVE

17．2 One-Factor Models

17．3 The Rendleman and Bartter Model

17．4 The Vasicek Model

17．5 The Cox， Ingersoll， and Ross Model

17．6 Two-Factor Models

17．7 Introduction to No-Arbitrage Models

17．8 Modeling Forward Rates

17．9 Developing Markov Models

17．10 Ho and Lee Model

17．11 Hull and White Model

17．12 Interest Rate Trees

17．13 A General Tree-Building Procedure

17．14 Nonstationary Models

17．15 Forward Rates and Futures Rates

17．16 Summary

Suggestions for Further Reading

Questions and Problems

18 EXOTIC OPTIONS

18．1 Types of Exotic Options

18 EXOTIC OPTIONS

18．3 Path-Dependent Derivatives

18．2 Basic Numerical Procedures

18．4 Lookback Options

18．5 Barrier Options

18．6 Options on Two Correlated Assets

18．7 Hedging Issues

18．8 Static Options Replication

18．9 Summary

Suggestions for Further Reading

Questions and Problems

19 ALTERNATIVES TO BLACK-SCHOLES FOR OPTION PRICING

19．1 Known Changes in the Interest Rate and Volatility

19 ALTERNATIVES TO BLACK-SCHOLES FOR OPTION PRICING

19．2 Merton s Stochastic Interest Rate Model

19．3 Pricing Biases

19．4 Alternative Models

19．5 Overview of Pricing Biases

19．6 Stochastic Volatility

19．7 How Black-Scholes Is Used in Practice

19．8 Implied Trees

19．9 Empirical Research

19．10 Summary

Suggestions for Further Reading

Questions and Problems

Appendix 19A Pricing Formulas for Altemative Models

20 CREDIT RISK AND REGULATORY CAPITAL

20 CREDIT RISK AND REGULATORY CAPITAL

20．1 Background

20．2 Adjusting the Prices of Options for Credit Risk

20．3 Contracts That Can Be Assets or Liabilities

20．4 Historical Default Experience

20．5 Valuation of Convertible Bonds

20．6 The BIS Capital Requirements

20．7 Reducing Exposure to Credit Risk

20．8 Summary

Suggestions for Further Reading

Questions and Problems

21．1 Riskless Hedges

21 REVIEW OF KEY CONCEPTS

21 REVIEW OF KEY CONCEPTS

21．2 Traded Securities versus Other Underlying Variables

21．3 Risk-Neutral Valuation

21．4 Those Big Losses

21．5 A Final Word

MAJOR EXCHANGES

GLOSSARY OF NOTATION

TABLE FOR N（x）WHENx≤0

TABLE FOR N（x）WHENx≥0

AUTHOR INDEX

SUBJECT INDEX