Derivative securitiesPDF电子书下载

PART Ⅰ THE BASICS 2

1 INTRODUCTION TO DERIVATIVE SECURITIES 2

1.0 Introduction 2

1.1 Forward Contracts 3

Formalization 4

1.2 Futures Contracts 6

Standardization 6

Clearing House 8

Settlement Price 9

Daily Settlement and Margins 10

Regulation 11

Why Standardization？Why Daily Settlement？ 11

Basis 12

Newspaper Quotes 13

1.3 Options 15

Call Options 15

Put Options 17

American versus European Options 19

1.4 Organized Option Markets 20

1.5 Option Newspaper Quotes 22

1.6 Interest Rates and Bond Prices 23

Zero-Coupon Bond Prices 23

Discount Rates 24

Simple Interest Rates 25

Discretely Compounded Interest Rates 26

Continuously Compounded Interest Rates 29

1.7 Summary 30

2 SIMPLE ARBITRAGE RELATIONSHIPS FOR FORWARD AND FUTURES CONTRACTS 34

2.0 Introduction 34

2.1 Definition of Arbitrage 34

2.2 Assumptions 35

2.3 Forward and Spot Prices 37

No Cash Flows on the Underlying Asset Over the Life of the Forward Contract 37

Formal Derivation （Cash-and-Carry） 39

Value of a Forward Contract 41

2.4 Known Cash Flows to the Underlying Asset 42

Formal Derivation 44

Value of a Forward Contract 46

2.5 Forward Contracts on Constant Dividend Yield and Interest-Paying Assets 47

Forward Contracts on a Stock Index 47

Foreign Exchange Forward Contracts 48

2.6 Forward Contracts on Commodities 51

Storage Costs 52

Convenience Yield 54

The Implied Repo Rate 55

Forward Contracts on Electricity 55

2.7 Forward and Futures Prices Compared 56

Equality of Forward and Futures Prices 59

Empirical Evidence 61

2.8 Summary 62

Appendix：Present Value of Dividends Over Life of Forward Contract 67

3 SIMPLE ARBITRAGE RELATIONSHIPS FOR OPTIONS 68

3.0 Introduction 68

3.1 Call and Put Options 68

3.2 Put Options 74

3.3 Relationship Between European Call and Put Options 79

3.4 Relationship Between American Call and Put Options 82

3.5 Summary 84

PART Ⅱ THE BINOMIAL MODEL 90

4 ASSET PRICE DYNAMICS 90

4.0 Introduction 90

4.1 The Lognormal Distribution 91

4.2 The Basic Idea （Binomial Pricing） 96

4.3 Formal Description （Binomial Pricing） 98

4.4 The Binomial Approximation to the Lognormal Distribution 99

4.5 Extensions 105

4.6 Stochastic Differential Equation Representation 105

4.7 Complications 107

Lognormal Distribution 107

Continuous Trading 107

Continuously Changing Prices 108

4.8 Summary 108

Appendix：The Expected Value of the Future Stock Price 112

5 THE BINOMIAL PRICING MODEL 114

5.0 Introduction 114

5.1 Single-Period Example 115

5.2 Multiperiod Example 119

5.3 The Binomial Pricing Model 123

The Binomial Model 123

Constructing the Synthetic Option 124

Risk-Neutral Valuation 126

Put Options 130

5.4 Hedge Ratio （Delta） 133

5.5 Lattice Parameters 133

5.6 The Black-Scholes Option Pricing Model 137

5.7 Forward and Futures Prices 138

Formalization 143

5.8 Replicating an Option on Spot with Futures 146

Formalization 148

Hedge Ratios 149

5.9 Summary 150

6 MARTINGALE PRICING 155

6.0 Introduction 155

6.1 Relative Prices and Martingales 155

The Money Market Account 156

Risk-Neutral Valuation 156

6.2 Martingales and No Arbitrage 157

6.3 Futures Prices 161

Formal Description 165

6.4 Summary 166

Appendix：Proof of the Proposition 171

7 AMERICAN OPTIONS 175

7.0 Introduction 175

7.1 Cum-Dividend/Ex-Dividend Prices 176

7.2 American Call Options 178

No Dividends 178

Dividends 181

7.3 American Put Options 183

Time Value 183

Dividends 185

7.4 Valuation 187

American Call Options 187

Computational Complexity 191

American Put Options 192

7.5 Options on Forward Contracts 195

Call Options 196

Put Options 198

Valuation 199

7.6 Summary 203

PART Ⅲ THE BLACK-SCHOLES MODEL AND EXTENSIONS 210

8 THE BLACK-SCHOLES MODEL 210

8.0 Introduction 210

8.1 Continuous Time Representation of Stock Price Changes 211

8.2 Interest Rates 213

8.3 Ito’s Lemma 213

8.4 The Equivalent Martingale Probability Distribution 215

8.5 European Options 217

8.6 Hedging 218

8.7 Properties of the Black-Scholes Model 224

8.8 Use of the Black-Scholes Model 227

Historic Volatility 228

Implied Volatility 231

8.9 Option Strategies 233

8.10 Partial Differential Equation 235

Derivation 235

Delta，Gamma，and Theta 236

8.11 Summary 237

Appendix A 245

Appendix B 247

Appendix C：Unequally Spaced Observations 248

Appendix D 249

9 EXTENSIONS TO THE BLACK-SCHOLES MODEL 251

9.0 Introduction 251

9.1 Known Dividend Model 251

9.2 Pseudo-American Model 255

9.3 The Roll Model 257

9.4 Constant Dividend Yield Model 258

9.5 Options on Futures and Forward Contracts 261

Futures Contracts 261

Forward Contracts 264

9.6 Summary 265

Appendix：Continuous Dividend Yield 271

10 REPLICATION AND RISK EXPOSURE WITH MODEL MISSPECIFICATION 272

10.0 Introduction 272

10.1 Problems with Delta Hedging 272

10.2 A General Approach 278

10.3 Delta Hedging 282

The Delta Neutral Position 283

Formalization 285

10.4 Delta-Gamma Hedging 286

Formalization 289

Theta Neutral 289

10.5 Delta-Gamma-Vega Hedging 290

Formalization 293

10.6 Model Misspecification 294

10.7 Summary 294

11 FOREIGN CURRENCY 302

11.0 Introduction 302

11.1 Foreign Currency Derivatives 302

Foreign Currency Options 303

Options on Foreign Currency Futures 305

Uses of Currency Derivatives 308

11.2 Single-Period Example 310

11.3 Multiperiod Extension 315

11.4 Formalization 318

Martingale Pricing 320

Risk-Neutral Valuation 320

Replicating Portfolio 320

11.5 Lattice Parameters 321

11.6 Closed Form Solutions （Modified Black-Scholes） 325

11.7 American Options 330

11.8 Options on Foreign Currency Futures 334

Closed Form Solutions 336

11.9 Replicating Options on Spot with Futures 338

11.10 Summary 342

Appendix：The Quadratic Approximation 349

12 STOCK INDEXES AND COMMODITIES 350

12.0 Introduction 350

12.1 Derivatives on Stock Market Indexes 350

12.2 Stock Market Index Futures 352

Futures Prices 352

12.3 Spread Trading 355

Same Index 355

Different Indexes 356

12.4 Index Options 357

12.5 Pricing Index Options 361

Binomial Pricing Model 362

Closed Form Solutions 364

Discrete Dividends 365

Synthetic Options 366

Circuit Breakers 368

The Wildcard Option 369

12.6 Options on Index Futures 369

Pricing Index Futures Options 371

12.7 Commodity Derivatives 372

Futures Prices 372

Futures Options 374

12.8 Summary 377

PART Ⅳ INTEREST RATE CONTRACTS，THE HJM MODEL，AND EXTENSIONS 386

13 INTEREST RATE CONTRACTS 386

13.0 Introduction 386

13.1 Zero-Coupon Bonds 386

Discount Rates 387

Simple Interest Rates 388

Continuously Compounded Interest Rates 389

13.2 Coupon Bonds 389

Pricing 390

Yield-to-Maturity 391

Quotes 393

Floating Rate Notes 396

13.3 The Term Structure of Default-Free Interest Rates 397

Forward Rates 397

Formalization 399

Par Bond Yield Curve 401

Computing the Zero-Coupon Yield Curve 403

13.4 Traditional Measures of Interest Rate Risk 404

Duration 404

Convexity 407

Limitations of Analysis 409

13.5 Treasury Bill Futures 410

13.6 Eurodollar Contracts 411

Eurodollar Deposits 411

Forward Rate Agreements （FRAs） 413

Formalization 414

Futures Contracts 416

13.7 Treasury Bond and Note Futures 418

The Delivery Process 420

13.8 Treasury Bond Futures 421

Conversion Factors 421

Cheapest to Deliver 423

Wild Card Option 424

Timing Option 425

13.9 Summary 425

Appendix：Duration and Convexity Correction for a Semiannual Coupon Bond 428

14 SWAPS 431

14.0 Introduction 431

14.1 Interest Rate Swaps 431

Pricing Schedules 433

Warehousing 434

Valuation 434

Par Swaps 437

Variants of Interest Rate Swaps 439

14.2 Foreign Currency Swaps 439

Valuation of Currency Swaps 441

Variants of Foreign Currency Swaps 444

14.3 Commodity Swaps 444

Valuation of Commodity Swaps 445

Variants of Commodity Swaps 446

14.4 Equity Swaps 447

Valuation 448

Variants of the Basic Equity Swaps 450

14.5 Summary 450

15 INTEREST RATE DERIVATIVES 455

15.0 Introduction 455

15.1 Construction of the Lattice 455

15.2 Spot Rate Process 463

Normal Distribution 463

Lognormal Distribution 468

15.3 Valuing Options on Treasury Bills 473

Put Options 474

A Replicating Portfolio 475

Call Options 477

Put-Call Parity 477

15.4 Treasury Bill Futures 478

Pricing 478

Hedging 480

15.5 Summary 482

16 PRICING TREASURY BILLS，TREASURY BONDS，TREASURY FUTURES，AND HEDGING WITH MODEL MISSPECIFICATION 487

16.0 Introduction 487

16.1 The Heath-Jarrow-Morton Model 488

The Forward Rate Evolution 488

The Spot Rate and Money Market Account Evolution 490

Zero-Coupon Bond Price Evolution 491

Arbitrage-Free Restrictions 492

Mean Reversion/Volatility Reduction 493

16.2 Hedging Treasury Bills 494

Hedge Ratio （Delta） 496

Gamma Hedging 500

Gamma and Convexity 501

16.3 Hedging Treasury Bonds 504

16.4 Treasury Bill Futures 506

Hedging 508

Hedge Ratio （Delta） 509

Gamma Hedging 512

16.5 Treasury Bond Futures 512

16.6 Summary 516

Appendix：Proof of the Results on Pages 492-493 520

17 PRICING INTEREST RATE OPTIONS AND HEDGING WITH MODEL MISSPECIFIGATION 522

17.0 Introduction 522

17.1 Options on Treasury Bills 522

Pricing 523

Hedging 525

17.2 Caps，Floors，and Collars 527

Caps and Caplets 527

Floors and Collars 531

The Black Model for Caps and Floors 533

17.3 Options on Treasury Bonds 537

Swaptions 539

17.4 Options on Treasury Bill Futures 544

17.5 Options on Treasury Bond Futures 547

17.6 Summary 551

18 CREDIT RISK 556

18.0 Introduction 556

18.1 Pricing Credit-Risky Bonds 557

Lattice of Default-Free Interest Rates 559

Risky Debt 560

Credit-Risky Debt 561

Formalization 568

Interpretation of Expression （18.10a，b） 571

Value of the Claim in the Event of Default 571

18.2 Pricing Options on Credit-Risky Bonds 571

Formalization 573

Hedging 573

18.3 Pricing Vulnerable Derivatives 575

Formalization 577

Hedging 580

Risk Management 581

18.4 Valuation of a Swap 581

Fixed Payment Side 581

Floating Payment Side 582

18.5 Credit Default Swaps 583

18.6 Regulation 587

Bank of International Settlement （B.I.S.） 1988 Accord 588

B.I.S.1996 Amendment 590

Limitations of the 1988 Accord and 1996 Amendment 591

18.7 What Can Go Wrong？ 592

Recipes for Risk 593

18.8 Summary 596

PART Ⅴ EXOTICS 602

19 NON-STANDARD （EXOTIC） OPTIONS 602

19.0 Introduction 602

19.1 European Digital （Binary） Options 602

Digital Call 602

Digital Put 603

Hedging 606

Gap Options 610

19.2 Paylater Options 612

Call Option 612

Put Option 615

19.3 Compound Options 616

Options on a Call 616

Options on a Put 618

19.4 Chooser Option 621

Special Case （T1=T2，K1=K2） 621

General Case 622

19.5 Options on the Minimum or Maximum of Two Risky Assets 623

Formalization 625

Call Option on the Minimum 625

Put Option on the Minimum 626

Call Option on the Maximum 627

Put Option on the Maximum 628

19.6 Summary 630

20 NON-STANDARD （EXOTIC） OPTIONS：PATH-DEPENDENT 635

20.0 Introduction 635

20.1 Barrier Options 635

Down-and-Out Options 635

Down-and-In Options 641

Up-and-Out Options 643

Up-and-In Options 646

20.2 Lookback Options 647

Standard Lookback Options 647

Options on Extrema 650

20.3 Average Options 653

20.4 Summary 659

GLOSSARY OF SYMBOLS 664

GLOSSARY OF TERMS 667

INDEX 677