Table of Contents
Foreword xiii
Preface xvii
About the Authors xix
Part One Introduction to Bonds 1
Chapter 1 The Bond Instrument 3
Chapter 2 Bond Instruments and Interest-Rate Risk 43
Appendix 2.1 Formal Derivation of Modified-Duration Measure 59
Appendix 2.2 Measuring Convexity 59
Appendix 2.3 Taylor Expansion of the Price/Yield Function 61
Chapter 3 Bond Pricing, Spot, and Forward Rates 65
Appendix 3.1 The Integral 83
Appendix 3.2 The Derivation of the Bond Price Equation in Continuous Time 85
Chapter 4 Interest-Rate Modelling 89
Appendix 4.1 Geometric Brownian Motion 101
Chapter 5 Fitting the Yield Curve 105
Appendix 5.1 Linear Regression: Ordinary Least Squares 124
Appendix 5.2 Regression Splines 127
Part Two Selected Market Instruments 133
Chapter 6 The Money Markets 135
Appendix 6.1 179
Chapter 7 Hybrid Securities and Structured Securities 181
Chapter 8 Bonds with Embedded Options and Option-Adjusted Spread Analysis 205
Appendix 8.1 Calculating Interest Rate Paths Using Microsoft Excel 232
Chapter 9 Inflation-Indexed Bonds and Derivatives 235
Appendix 9.1 Current Issuers of Public-Sector Indexed Securities 256
Appendix 9.2 U.S. Treasury Inflation-Indexed Securities (TIPS) 257
Chapter 10 Introduction to Securitisation and Asset-Backed Securities 261
Part Three Derivative Instruments 297
Chapter 11 Forwards and Futures Valuation 299
Chapter 12 Bond Futures Contracts 309
Appendix 12.1 The Conversion Factor for the Long Gilt Future 324
Chapter 13 Swaps 329
Appendix 13.1 Calculating Futures Strip Rates and Implied Swap Rates 370
Chapter 14 Credit Derivatives I: Instruments and Applications 375
Appendix 14.1 Bond Credit Ratings 418
Chapter 15 Credit Derivatives II: Pricing, Valuation, and the Basis 421
Chapter 16 Options I 435
Appendix 16.1 Summary of Basic Statistical Concepts 456
Appendix 16.2 Lognormal Distribution of Returns 457
Appendix 16.3 Black-Scholes Model in Microsoft Excel 458
Chapter 17 Options II 461
Part Four Bond Trading and Hedging 475
Chapter 18 Value-at-Risk and Credit VaR 477
Appendix 18.1 Assumption of Normality 513
Chapter 19 Government Bond Analysis, the Yield Curve, and Relative-Value Trading 517
Chapter 20 Approaches to Trading and Hedging 551
Appendix 20.1 Summary of Derivation of Optimum Hedge Equation 571
Appendix 20.2 Forward-Rate Structure in Conventional Yield-Curve Environment 571
Chapter 21 Derivatives Risk Management: Convexity, Collateral, and Correlation 573
Appendix A Statistical Concepts 621
Appendix B Basic Tools 627
Appendix C Introduction to the Mathematics of Fixed-Income Pricing 633
Appendix D About the Companion Website 639
Glossary 641
Index 669