Fixed Income Markets: Management, Trading and Hedging

Praise for Fixed Income Markets Second Edition One of the most comprehensive and detailed books on fixed income securities you will find. A must–read whether youre new to fixed income or youre a seasoned investment professional. Patrick Y. Shim, CG Investment Group, Wells Fargo Advisors LLC, Los Angeles Another fabulous guide to the fixed income markets from Moorad that will serve readers from all backgrounds very well. The authors writing style is always entertaining, yet practical for all market participants, focusing and delivering on the latest concepts and strategies in the fixed income space that come from being a seasoned practitioner himself. Stuart Turner, Senior Treasury Dealer, Newedge UK Financial Ltd, London The first edition has been widely praised for its clarity and precision, its practical and pragmatic approach and its comprehensive coverage of risk management and trading in fixed income markets. This second edition updates the existing text and contains essential new material, particularly on some of the latest structured credit OTC products. I recommend it without reservation to both practitioners and academics, especially those involved in masters courses on fixed income cash and derivatives markets. Carol Alexander, Professor of Finance and Head of Business and Management Department, University of Sussex and co–editor–in–chief of the Journal of Banking and Finance A very welcome new edition of Professor Choudhrys benchmark bond and fixed income markets textbook. There is excellent coverage of the latest developments in both cash and derivatives products, and very useful detail on the impact of issues such as greater collateral and secured funding requirements. A high–quality reference book written in the authors trademark accessible style, which will be of great value to those involved in the debt capital markets in any capacity. Mohamoud Barre Dualeh, Head of Product Development, Alizz Islamic Bank, Muscat A welcome update with this second edition, and again a very pedagogical contribution from Moorad Choudhry, of immense interest both for students and practitioners. Exactly what you need to master the bond markets. Philippe Priaulet, Head of the Shareholders Network Sales Desk, Natixis, Paris and Associate Professor, University of Evry Val dEssonne

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 Modifi ed–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 Infl ation–Indexed Bonds and Derivatives 235 Appendix 9.1 Current Issuers of Public–Sector Indexed Securities 256 Appendix 9.2 U.S. Treasury Infl ation–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

MOORAD CHOUDHRY works in Group Treasury at The Royal Bank of Scotland, and is a Professor at the Department of Mathematical Sciences, Brunel University. He was a UK government bond trader and money markets trader with ABN Amro Hoare Govett Securities Ltd and a sterling proprietary trader with Hambros Bank Limited. He later traded structured finance bonds and repo at KBC Financial Products. Moorad lives in Surrey, England. DAVID MOSKOVIC is a hybrid derivatives trader at The Royal Bank of Scotland. Prior to that he worked in market risk and as a quantitative analyst. He qualified as a Chartered Accountant at Ernst Young before moving to RBS. MAX WONG is Head of Risk Model Validation at The Royal Bank of Scotland in Singapore. He was previously an index futures trader on the open–outcry floor at SIMEX and a risk quant at Standard Chartered. He is author of Bubble Value at Risk: A Countercyclical Risk Management Approach .