Foreword xv
Preface xvii
Part One Introduction To Bonds
1 The Bond Instrument 3
The Time Value of Money 4
Basic Features and Definitions 5
Present Value and Discounting 6
Discount Factors 12
Bond Pricing and Yield: The Traditional Approach 15
Bond Pricing 16
Bond Yield 20
Floating Rate Notes 27
Accrued Interest 30
Clean and Dirty Bond Prices 30
Day-Count Conventions 32
2 Bond Instruments and Interest Rate Risk 35
Duration, Modified Duration, and Convexity 35
Duration 36
Properties of Macaulay Duration 40
Modified Duration 41
Convexity 45
3 Bond Pricing and Spot and Forward Rates 51
Zero-Coupon Bonds 51
Coupon Bonds 53
Bond Price in Continuous Time 55
Fundamental Concepts 55
Stochastic Rates 58
Coupon Bonds 60
Forward Rates 61
Guaranteeing a Forward Rate 61
The Spot and Forward Yield Curve 63
Calculating Spot Rates 64
Term Structure Hypotheses 67
The Expectations Hypothesis 67
Liquidity Premium Hypothesis 69
Segmented Markets Hypothesis 69
4 Interest Rate Modeling 71
Basic Concepts 71
Short-Rate Processes 72
Ito's Lemma 74
One-Factor Term-Structure Models 75
Vasicek Model 75
Hull-White Model 76
Further One-Factor Term-Structure Models 77
Cox-Ingersoll-Ross (CIR) Model 78
Two-Factor Interest Rate Models 79
Brennan-Schwartz Model 80
Extended Cox-Ingersoll-Ross Model 80
Heath-Jarrow-Morton (HJM) Model 81
The Multifactor HJM Model 82
Choosing a Term-Structure Model 83
5 Fitting the Yield Curve 87
Yield Curve Smoothing 88
Smoothing Techniques 90
Cubic Polynomials 91
Non-Parametric Methods 92
Spline-Based Methods 92
Nelson and Siegel Curves 95
Comparing Curves 96
Fitting the Term Structure of Interest Rates: The Practical Implementation of Cubic Spline Methodology 96
Cubic Spline Methodology 97
The Hypothesis 99
Practical Approach 100
A Working Environment 100
The First Requirement 101
The Second Requirement 101
The Third Requirement 102
Meeting All Requirements Simultaneously 102
A Unique Solution 103
The Solution 108
A Look at Forward Rates 114
Conclusion 117
Part Two Selected Cash and Derivative Instruments
6 Forwards and Futures Valuation 121
Forwards and Futures 121
Cash Flow Differences 122
Relationship Between Forward and Futures Prices 124
Forward-Spot Parity 125
The Basis and Implied Repo Rate 127
7 Swaps 131
Interest Rate Swaps 132
Market Terminology 134
Swap Spreads and the Swap Yield Curve 135
Generic Swap Valuation 138
Intuitive Swap Pricing 138
Zero-Coupon Swap Valuation 139
Calculating the Forward Rate from Spot-Rate Discount Factors 139
The Key Principles of an Interest Rate Swap 143
Valuation Using the Final Maturity Discount Factor 143
Non-Plain Vanilla Interest Rate Swaps 146
Swaptions 148
Valuation 149
Interest Rate Swap Applications 150
Corporate and Investor Applications 150
Hedging Bond Instruments Using Interest Rate Swaps 153
8 Options 157
Option Basics 158
Terminology 160
Option Instruments 162
Option Pricing: Setting the Scene 164
Limits on Option Prices 165
Option Pricing 166
The Black-Scholes Option Model 168
Assumptions 169
Pricing Derivative Instruments Using the Black-Scholes Model 170
Put-Call Parity 173
Pricing Options on Bonds Using the Black-Scholes Model 174
Interest Rate Options and the Black Model 174
Comments on the Black-Scholes Model 180
Stochastic Volatility 180
Implied Volatility 180
Other Option Models 181
9 Measuring Option Risk 183
Option Price Behavior 183
Assessing Time Value 183
American Options 184
The Greeks 185
Delta 185
Gamma 187
Theta 189
Vega 189
Rho 190
Lambda 192
The Option Smile 193
Caps and Floors 194
10 Credit Derivatives 197
Credit Risk 198
Credit Risk and Credit Derivatives 200
Applications of Credit Derivatives 201
Credit Derivative Instruments 202
Credit Default Swap 202
Credit Options 203
Credit-Linked Notes 204
Total Return Swaps 205
Investment Applications 207
Capital Structure Arbitrage 209
Exposure to Market Sectors 210
Credit Spreads 210
Funding Positions 210
Credit Derivatives and Relative Value Trading 212
Relative Value Trading Strategies 212
Bond Valuation from CDS Prices: Bloomberg Screen VCDS 217
Credit-Derivative Pricing 218
Pricing Total Return Swaps 218
Asset-Swap Pricing 219
Credit-Spread Pricing Models 219
The Market Approach to CDS Pricing 220
Default Probabilities 220
Pricing a CDS Contract 226
Example Calculation 228
The ITraxx and CD-X Credit Indices Contracts 229
Index Tranche Market 236
Impact of the 2007-2008 Credit Crunch: New CDS Contracts 240
11 The Analysis of Bonds with Embedded Options 245
Understanding Option Elements Embedded in a Bond 245
Basic Options Features 246
Option Valuation 247
The Call Provision 248
The Binomial Tree of Short-Term Interest Rates 249
Arbitrage-Free Pricing 250
Options Pricing 252
Risk-Neutral Pricing 254
Recombining and Nonrecombining Trees 255
Pricing Callable Bonds 256
Price and Yield Sensitivity 261
Measuring Bond Yield Spreads 263
12 Option-Adjusted Spread Analysis 265
Introduction 265
A Theoretical Framework 266
The Methodology in Practice 272
13 Convertible Bonds 277
Basic Features 277
Trading Patterns of Convertible Bonds 279
Investor Analysis 280
Zero-Coupon Convertibles 284
Convertible Bond Default Risk 285
Advantages of Issuing and Holding Convertibles 285
Convertible Bond Valuation 288
Fair Value of a Convertible Bond: The Binomial Model 288
Model Parameters 297
Pricing Spreadsheet 299
14 Inflation-Indexed Bonds 303
Basic Concepts 303
Choice of Index 303
Indexation Lag 305
Coupon Frequency 306
Type of Indexation 306
Index-Linked Bond Cash Flows and Yields 308
TIPS Cash Flow Calculations 309
TIPS Price and Yield Calculations 309
Assessing Yields on Index-Linked Bonds 313
Which to Hold: Indexed or Conventional Bonds? 314
Analysis of Real Interest Rates 315
Indexation Lags and Inflation Expectations 315
An Inflation Term Structure 317
Inflation-Indexed Derivatives 318
15 Securitization and Asset-Backed Securities 327
The Concept of Securitization 328
Reasons for Undertaking Securitization 328
Benefits of Securitization to Investors 330
The Process of Securitization 331
Securitization Process 331
Credit Enhancement 335
Securitizing Mortgages 336
Growth of the Market 337
Mortgage Bond Risk 338
Types of Mortgage-Backed Securities 338
Cash Flow Patterns 339
Prepayment Analysis 340
Prepayment Models 344
ABS Structures: A Primer on Performance Metrics and Test Measures 345
Collateral Types 345
Summary of Performance Metrics 351
Securitization: Features of the 2007-2009 Financial Crisis 351
Impact of the Credit Crunch 351
16 Collateralized Debt Obligations 357
CDO Structures 359
Conventional CDO Structures 359
Synthetic CDO Structures 360
Motivation Behind CDO Issuance 362
Balance Sheet-Driven Transactions 362
Investor-Driven Arbitrage Transactions 363
Analysis and Evaluation 363
Portfolio Characteristics 363
Cash Flow Analysis and Stress Testing 364
Originator's Credit Quality 365
Operational Aspects 365
Legal Structure of the Transaction 365
Expected Loss 366
CDO Market Overview Since 2005 366
Risk and Capital Management 368
Part Three Selected Market Trading Considerations
17 The Yield Curve, Bond Yield, and Spot Rates 373
Practical Uses of Redemption Yield and Duration 373
The Concept of Yield 374
Yield Comparisons in the Market 376
Measuring a Bond's True Return 376
Illustrating Bond Yield Using a Microsoft Excel Spreadsheet 380
Implied Spot Rates and Market Zero-Coupon Yields 388
Spot Yields and Coupon-Bond Prices 389
Implied Spot Yields and Zero-Coupon Bond Yields 393
Determining Strip Values 394
Strips Market Anomalies 395
Strips Trading Strategy 396
Case Study: Treasury Strip Yields and Cash Flow Analysis 399
18 Approaches to Trading 401
Futures Trading 402
Yield Curves and Relative Value 406
Determinants of Government Bond Yields 406
Characterizing the Complete Term Structure 408
Identifying Relative Value in Government Bonds 409
Hedging Bond Positions 412
Simple Hedging Approaches 412
Hedge Analysis 413
Summary of the Derivation of the Optimum-Hedge Equation 415
19 Credit Analysis and Relative Value Measurement 417
Credit Ratings 418
Purpose of Credit Ratings 418
Formal Credit Ratings 419
Credit Analysis 420
The Issuer Industry 421
Financial Analysis 423
Industry-Specific Analysis 426
Utility Companies 426
Financial Sector Companies 427
The Art of Credit Analysis 428
Bond Spreads and Relative Value 429
Bond Spreads 429
Summary of Fund Managers' Approach to Value Creation 438
Appendix I: The Black-Scholes Model in Microsoft Excel 443
Appendix II: Iterative Formula Spreadsheet 445
Appendix III: Pricing Spreadsheet 447
References 451
About the Author 463
Index 465
