Interest Rate Swaps and Other Derivatives

Interest Rate Swaps and Other Derivatives

by Howard Corb

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Overview

The first swap was executed over thirty years ago. Since then, the interest rate swaps and other derivative markets have grown and diversified in phenomenal directions. Derivatives are used today by a myriad of institutional investors for the purposes of risk management, expressing a view on the market, and pursuing market opportunities that are otherwise unavailable using more traditional financial instruments. In this volume, Howard Corb explores the concepts behind interest rate swaps and the many derivatives that evolved from them.

Corb's book uniquely marries academic rigor and real-world trading experience in a compelling, readable style. While it is filled with sophisticated formulas and analysis, the volume is geared toward a wide range of readers searching for an in-depth understanding of these markets. It serves as both a textbook for students and a must-have reference book for practitioners. Corb helps readers develop an intuitive feel for these products and their use in the market, providing a detailed introduction to more complicated trades and structures. Through examples of financial structuring, readers will come away with an understanding of how derivatives products are created and how they can be deconstructed and analyzed effectively.

Product Details

ISBN-13: 9780231159647
Publisher: Columbia University Press
Publication date: 08/28/2012
Series: Columbia Business School Publishing
Pages: 624
Product dimensions: 8.70(w) x 6.20(h) x 1.80(d)
Age Range: 18 Years

About the Author

Howard Corb is an adjunct associate professor in finance and economics at Columbia Business School and a partner at Arel Capital. After receiving his Ph.D. in finance from Stanford University, he began his Wall Street career at J. P. Morgan and later joined Morgan Stanley, during which time he worked with a variety of institutional clients to help manage their interest rate risk using derivatives.

Table of Contents

Preface xiii

Acknowledgments xvii

List of Abbreviations xix

1 An Introduction to Swaps 1

1.1 Overview 1

1.2 Swaps 3

1.2.1 Fixed-Floating Swaps 4

1.2.2 Basis Swaps 28

1.2.3 Cross-Currency Swaps 34

2 The Risk Characteristics and the Traditional Uses of Swaps 40

2.1 Interest Rate Risk 40

2.1.1 PV01 43

2.2 Spread Risk 48

2.2.1 A Closer Look at Swap Spreads 50

2.3 Currency Risk 57

2.4 Counterparty Risk 58

2.5 Traditional Uses of Swaps 63

2.5.1 New Issue Hedging 63

2.5.2 Asset Swaps 68

2.5.3 Balance Sheet Management 70

3 The Pricing of Swaps 76

3.1 Where Do Swap Rates Come From? 76

3.1.1 The Link Between Swap Rates and Eurodollar Futures 79

3.1.2 The Futures Convexity Bias 84

3.2 Moving On: Bootstrapping the Curve and Creating a Swap Model 86

3.2.1 A Stylized Example 89

3.2.2 PV01s in Our Stylized Example 102

3.3 Moving On: Pricing Up Nonstandard Swaps 102

3.3.1 Mark-to-Markets 104

3.3.2 Unwinds 111

3.3.3 Assignments 112

3.3.4 Forward Starting Swaps 113

4 Caps and Floors 135

4.1 An Introduction to Caps and Floors 135

4.1.1 Cap-Floor Parity 137

4.1.2 Uses of Caps and Floors 138

4.1.3 An Embedded Cap Trade 140

4.1.4 Valuing Caps and Floors 142

4.1.5 Vol 144

4.1.6 Valuing Caps and Floors in Our Stylized Model 147

4.1.7 Variations of Standard Caps and Floors 150

5 Swaptions 166

5.1 An Introduction to Swaptions 166

5.1.1 The Value of Swaptions at Expiration 168

5.1.2 Swaption Parity 169

5.1.3 Uses of Swaptions 170

5.1.4 Valuing Swaptions Using Black's Formula 172

5.1.5 Swaption Vol 174

5.1.6 Pricing Swaptions in Our Stylized Example 175

5.2 The Link Between Caps/Floors and Swaptions 178

5.3 Questioning Black's Model for Interest Rate Options 180

5.3.1 Are Interest Rates Lognormal? 181

5.3.2 Swaption Prices and Implied Vol 184

5.3.3 Skew 184

5.4 The Normal Model 193

5.4.1 Background 193

5.4.2 The Model 194

5.4.3 Pricing Under the Normal Model 195

5.4.4 Relationship Between Normal Implied Vol and Lognormal Implied Vol for At-the-Money Swaptions 198

5.4.5 Explaining Skew: The Relationship Between Normal Implied Vol and Lognormal Implied Vol for Off-the-Money Swaptions 205

5.4.6 The Normal Model: The Industry Standard 206

5.5 Other Models Used to Price Interest Plate Options 208

5.6 Bermudan Swaptions 209

5.6.1 Optimal Exercise of Bermudan Swaptions 211

5.6.2 Valuation of Bermudan Swaptions 217

6 Swaps with Embedded Options 230

6.1 An Underlying Concept 230

6.2 Cancelable Swaps 232

6.2.1 Some Uses of Cancelable Swaps 234

6.2.2 Solving for the Fixed Rate in Cancelable Swaps 235

6.2.3 Bermudan Cancelables 242

6.3 Index Amortizing Swaps 248

6.3.1 An Explanation of the Trade 250

6.3.2 Pricing Index Amortizing Swaps 252

6.3.3 Relationship Between Index Amortizing Swaps and Cancelable Swaps 253

6.4 Knockout Swaps 256

6.5 Swaps with Convexity Adjustments 262

6.5.1 LIBOR in Arrears Swaps 262

6.5.2 CMS Swaps 273

7 Structured Notes 292

7.1 The Rise of the Structured Note Market 294

7.2 A Glossary of Structured Notes 295

7.3 Size of the Market 299

7.4 What Are Structured Notes? 300

7.5 In the Beginning … Floating Rate Notes 305

7.5.1 A Prime Floating Rate Note 305

7.6 Capped Floaters 308

7.6.1 An Example: Pricing Up a Capped Floater 309

7.7 Inverse Floaters 310

7.7.1 An Example: Pricing Up a Leveraged Inverse Floater 315

7.7.2 Orange County 321

7.8 Range Notes 324

7.8.1 LEANs 324

7.8.2 Binary Accrual Notes 326

7.9 Regulatory Response 331

7.10 Non-Inversion Notes 332

7.10.1 The Pricing of Non-Inversion Notes 333

8 Relative Value and Macro Trades 353

8.1 Carry and Roll-Down Analysis 354

8.2 Curve Trades 361

8.2.1 Yield Curve Trades for Longer Holding Periods 367

8.2.2 Forward Yield Curve Trades 373

8.2.3 Conditional Yield Curve Trades 376

8.3 Trading Swap Spreads 382

8.3.1 Spread Trades for Longer Holding Periods 385

8.3.2 Spread of Spread Trades 387

8.3.3 Conditional Spread Trades 389

8.4 Asset Swaps Revisited 394

8.4.1 Asset Swap Math 398

8.4.2 Asset Swaps Today 400

9 More Recent Product Innovations 414

9.1 An Introduction to Correlation Trades: Caps Versus Payer Redux 415

9.2 Forward Vol Trades 416

9.2.1 Preliminary 417

9.2.2 Description of Forward Vol 419

9.2.3 Heuristic Pricing of Forward Vol Trades 421

9.2.4 Will the Forward Price Be Higher or Lower Than the Spot Price? 424

9.2.5 Are Forward Vol Trades Truly a Pure View on Vol? 425

9.2.6 Bermudan Cancelable Swaps Revisited 426

9.3 Curve Options 427

9.3.1 Why Did Curve Options Come About? 430

9.3.2 Implied Correlation 433

9.3.3 Implied Volatility Versus Realized Volatility 434

9.3.4 Supply and Demand of Curve Options 436

9.3.5 The Pricing of Curve Options 437

9.3.6 A Couple of Trades 442

9.3.7 Delta Hedging Curve Options 450

9.3.8 So Why Did 30-Year Swap Spreads Go Negative - and What Does That Have to Do with Curve Options? 453

Appendixes 463

A Refresher in Option Pricing 463

A.1 The Basics 463

A.2 Boundaries on Option Prices 468

A.3 European Put-Call Parity 474

A.4 Binomial Pricing 475

A.4.1 Multiperiod Extensions 481

A.5 The Black-Scholes Formula 483

A.6 Option Sensitivities 488

A.6.1 Delta 488

A.6.2 Gamma 492

A.6.3 Vega 497

A.6.4 Theta 499

A.7 Binary Options 500

A.7.1 Delta of Binary Options 503

A.7.2 Vega of Binary Options 508

A.8 Packages 510

B A Brief Review of Some Fixed Income Topics 519

B.1 Present Value 519

B.2 Duration 520

B.2.1 Macaulay Duration 520

B.2.2 Modified Duration 521

B.2.3 Effective Duration 522

C A Closer Look at Day Count and Payment Conventions in Swaps 523

D A Quick Look at Mortgages 529

E The Normal Model 537

E.1 The Relationship Between σLN and σN for Swaptions that Are Struck At-the-Money Forward 539

E.2 The Relationship Between σLN and σLN for Off-the-Money Swaptions 541

E.3 Option Sensitivities Under the Normal Model 543

Solutions to Selected Problems 545

Bibliography 585

Index 589

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