Moorad Choudhry (Surrey, UK) is head of treasury at Europe Arab Bank plc in London. Previously, he was head of treasury at KBC Financial Products, and a vice president in Structured Finance Service at JPMorgan Chase Bank. Prior to that, he was a sterling proprietary trader at Hambros Bank Limited and gilt-edged market maker and money markets trader at ABN Amro Hoare Govett Ltd. Choudhry is visiting professor at the Department of Economics, London Metropolitan University and a visiting research fellow at the ICMA Centre, University of Reading. He was educated at the University of Westminster and the University of Reading. He obtained his MBA from Henley Management School and his PhD from Birkbeck, University of London. He has written several books on the credit markets.

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...