Fixed-Income Securities

Lionel Martellini is an assistant Professor of Finance at the Marshall School of Business, University of Southern California, where he teaches "fixed-income securities" at the MBA level. He is also a research associate at the EDHEC Risk and Asset Management Research Center, and a member of the editorial boards of The Journal of Bond Training and Management and The Journal of Alternative Investments. Philippe Priaulet is a fixed-income strategist in charge of derivatives strategies for HSBC. His expertise is related to fixed-income asset management and derivatives pricing and hedging, and his research has been published in leading academic and practitioners' journals. Formerly, he was head of fixed-income research in the Research and Innovation Department of HSBC-CCF.Stéphanie Priaulet is a senior index portfolio manager in the Structured Asset Management Department at AXA Investment Managers. Previously, he was head of qualitative engineering in The Fixed Income Research Department at AXA Investment Managers. He also teaches "fixed-income securities" as a part-time lecturer at the University Paris Dauphine. He is a member of the editorial board of The Journal of Bond Trading and Management, where he has published several research papers.

• About the Authors xixPreface xxiAcknowledgments xxvNotation xxviiPart I Investment Environment1 Bonds and Money-Market Instruments 31.1 Bonds 31.1.1 General Characteristics of Bonds 31.1.2 Bonds by Issuers 171.2 Money-Market Instruments 251.2.1 Definition 251.2.2 The Role of the Central Bank 251.2.3 T-Bills 261.2.4 Certificates of Deposit 281.2.5 Bankers’ Acceptances 291.2.6 Commercial Papers 291.2.7 Interbank Deposits 301.2.8 Repo and Reverse Repo Market Instruments 301.3 End of Chapter Summary 321.4 References and Further Reading 331.4.1 Books and Papers 331.4.2 Websites and Others 331.5 Problems 341.5.1 Problems on Bonds 341.5.2 Problems on Money-Market Instruments 361.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan Corporate Bond Markets 372 Bond Prices and Yields 412.1 Introduction to Bond Pricing 412.2 Present Value Formula 432.2.1 Time-Value of Money 432.2.2 The Mathematics of Discounting 432.2.3 Nominal versus Real Interest Rates 452.2.4 Time Basis and Compounding Frequency Conventions 462.2.5 Continuous Compounding 472.3 Taxonomy of Rates 492.3.1 Coupon Rate and Current Yield 492.3.2 Yield to Maturity 492.3.3 Spot Zero-Coupon (or Discount) Rate 512.3.4 Forward Rates 522.3.5 Bond Par Yield 542.4 End of Chapter Summary 542.5 References and Further Reading 542.6 Problems 55Part II Term Structure of Interest Rates3 Empirical Properties and Classical Theories of the Term Structure 633.1 Definition and Properties of the Term Structure 633.1.1 What Kind of Shape Can It Take? 653.1.2 How Does It Evolve over Time? 683.2 Classical Theories of the Term Structure 813.2.1 The Pure Expectations Theory 823.2.2 The Pure Risk Premium Theory 833.2.3 The Market Segmentation Theory 853.2.4 The Biased Expectations Theory: An Integrated Approach 863.2.5 Illustration and Empirical Validation 863.2.6 Summary and Extensions 873.3 End of Chapter Summary 883.4 References and Further Reading 893.4.1 On the Empirical Behavior of the Yield Curve 893.4.2 On the Principal Component Analysis of the Yield Curve 903.4.3 On the Classical Theories of the Term Structure of Interest Rates 903.5 Problems 914 Deriving the Zero-Coupon Yield Curve 964.1 Deriving the Nondefault Treasury Zero-Coupon Yield Curve 964.1.1 How to Select a Basket of Bonds? 964.1.2 Direct Methods 974.1.3 Indirect Methods 1034.2 Deriving the Interbank Zero-Coupon Rate Curve 1304.2.1 How to Select the Basket of Instruments? 1304.2.2 Interpolation Methods 1324.2.3 Least Squares Methods Based on Rates 1324.2.4 Least Squares Methods Based on Prices 1334.3 Deriving Credit Spread Term Structures 1364.3.1 Disjoint Methods 1364.3.2 Joint Methods 1374.4 End of Chapter Summary 1424.5 References and Further Reading 1444.6 Problems 1464.7 Appendix: A Useful Modified Newton’s Algorithm 155Part III Hedging Interest-Rate Risk5 Hedging Interest-Rate Risk with Duration 1635.1 Basics of Interest-Rate Risk: Qualitative Insights 1635.1.1 The Five Theorems of Bond Pricing 1635.1.2 Reinvestment Risk 1645.1.3 Capital Gain Risk 1655.1.4 Qualifying Interest-Rate Risk 1665.2 Hedging with Duration 1675.2.1 Using a One-Order Taylor Expansion 1675.2.2 Duration, $Duration and Modified Duration 1705.2.3 How to Hedge in Practice? 1735.3 End of Chapter Summary 1755.4 References and Further Reading 1765.4.1 Books 1765.4.2 Papers 1765.5 Problems 1776 Beyond Duration 1826.1 Relaxing the Assumption of a Small Shift 1826.1.1 Using a Second-Order Taylor Expansion 1826.1.2 Properties of Convexity 1856.1.3 Hedging Method 1876.2 Relaxing the Assumption of a Parallel Shift 1886.2.1 A Common Principle 1886.2.2 Regrouping Risk Factors through a Principal Component Analysis 1926.2.3 Hedging Using a Three-Factor Model of the Yield Curve 1956.3 End of Chapter Summary 1996.4 References and Further Reading 2006.5 Problems 201Part IV Investment Strategies7 Passive Fixed-Income Portfolio Management 2137.1 Straightforward Replication 2137.2 Replication by Stratified Sampling 2147.3 Tracking-Error Minimization 2167.3.1 Optimization Procedure 2167.3.2 Bond Return Covariance Matrix Estimation 2177.4 Factor-Based Replication 2267.5 Derivatives-Based Replication 2297.6 Pros and Cons of Stratified Sampling versus Tracking-Error Minimization 2307.7 End of Chapter Summary 2307.8 References and Further Reading 2317.8.1 Books and Papers 2317.8.2 Websites 2317.9 Problems 2318 Active Fixed-Income Portfolio Management 2338.1 Market Timing: Trading on Interest-Rate Predictions 2338.1.1 Timing Bets on No Change in the Yield Curve or “Riding the Yield Curve” 2348.1.2 Timing Bets on Interest-Rate Level 2368.1.3 Timing Bets on Specific Changes in the Yield Curve 2388.1.4 Scenario Analysis 2518.1.5 Active Fixed-Income Style Allocation Decisions 2558.2 Trading on Market Inefficiencies 2688.2.1 Trading within a Given Market: The Bond Relative Value Analysis 2698.2.2 Trading across Markets: Spread and Convergence Trades 2768.3 End of Chapter Summary 2828.4 References and Further Reading 2838.4.1 On Active Fixed-Income Strategies 2838.4.2 On Active Asset Allocation Decisions 2848.4.3 Others 2868.5 Problems 2869 Performance Measurement on Fixed-Income Portfolios 2939.1 Return Measures 2939.1.1 Arithmetic Rate of Return 2939.1.2 Geometric Rate of Return 2949.2 Risk-Adjusted Performance Evaluation 2959.2.1 Absolute Risk-Adjusted Performance Evaluation 2969.2.2 Relative Risk-Adjusted Performance Evaluation 2999.3 Application of Style Analysis to Performance Evaluation of Bond Portfolio Managers: An Example 3099.3.1 Alpha Analysis 3109.3.2 Passive Versus Active Managers 3139.4 End of Chapter Summary 3149.5 References and Further Reading 3159.5.1 Books and Papers 3159.5.2 Websites 3169.6 Problems 316Part V Swaps and Futures10 Swaps 32510.1 Description of Swaps 32510.1.1 Definition 32510.1.2 Terminology and Conventions 32510.2 Pricing and Market Quotes 32610.2.1 Pricing of Swaps 32610.2.2 Market Quotes 33310.3 Uses of Swaps 33410.3.1 Optimizing the Financial Conditions of a Debt 33510.3.2 Converting the Financial Conditions of a Debt 33610.3.3 Creating New Assets Using Swaps 33710.3.4 Hedging Interest-Rate Risk Using Swaps 33910.4 Nonplain Vanilla Swaps 34210.4.1 Accrediting, Amortizing and Roller Coaster Swaps 34210.4.2 Basis Swap 34310.4.3 Constant Maturity Swap and Constant Maturity Treasury Swap 34310.4.4 Forward-Starting Swap 34410.4.5 Inflation-Linked Swap 34410.4.6 Libor in Arrears Swap 34410.4.7 Yield-Curve Swap 34510.4.8 Zero-Coupon Swap 34510.5 End of Chapter Summary 34610.6 References and Further Reading 34610.6.1 Books and Papers 34610.6.2 Websites 34710.7 Problems 34711 Forwards and Futures 35311.1 Definition 35311.2 Terminology, Conventions and Market Quotes 35411.2.1 Terminology and Conventions 35411.2.2 Quotes 35611.3 Margin Requirements and the Role of the Clearing House 35811.4 Conversion Factor and the Cheapest-to-Deliver Bond 35911.4.1 The Cheapest to Deliver on the Repartition Date 36011.4.2 The Cheapest to Deliver before the Repartition Date 36111.5 Pricing of Forwards and Futures 36211.5.1 Forward-Spot Parity or How to Price a Forward Contract? 36211.5.2 The Forward Contract Payoff 36411.5.3 Relation between Forward and Futures Prices 36511.6 Uses of Forwards and Futures 36511.6.1 Pure Speculation with Leverage Effect 36511.6.2 Fixing Today the Financial Conditions of a Loan or Investment in the Future 36611.6.3 Detecting Riskless Arbitrage Opportunities Using Futures 36711.6.4 Hedging Interest-Rate Risk Using Futures 36811.7 End of Chapter Summary 37011.8 References and Further Reading 37111.8.1 Books and Papers 37111.8.2 Websites of Futures Markets and of the Futures Industry Association 37111.9 Problems 37211.10 Appendix: Forward and Futures Prices Are Identical When Interest Rates Are Constant 375Part VI Modeling The Term Structure of Interest Rates and Credit Spreads12 Modeling the Yield Curve Dynamics 38112.1 The Binomial Interest-Rate Tree Methodology 38212.1.1 Building an Interest-Rate Tree 38212.1.2 Calibrating an Interest-Rate Tree 38412.2 Continuous-Time Models 38712.2.1 Single-Factor Models 38812.2.2 Multifactor Models 39212.3 Arbitrage Models 39612.3.1 A Discrete-Time Example: Ho and Lee’s Binomial Lattice 39612.3.2 Arbitrage Models in Continuous Time 40112.4 End of Chapter Summary 40612.5 References and Further Reading 40712.6 Problems 41112.7 Appendix 1: The Hull and White Trinomial Lattice 41312.7.1 Discretizing the Short Rate 41312.7.2 Calibrating the Lattice to the Current Spot Yield Curve 41612.7.3 Option Pricing 41912.8 Appendix 2: An Introduction to Stochastic Processes in Continuous Time 42012.8.1 Brownian Motion 42012.8.2 Stochastic Integral 42312.8.3 Stochastic Differential Equations (SDE) 42512.8.4 Asset Price Process 42612.8.5 Representation of Brownian Martingales 42612.8.6 Continuous-Time Asset Pricing 42712.8.7 Feynman–Kac Formula 43112.8.8 Application to Equilibrium Models of the Term Structure 43213 Modeling the Credit Spreads Dynamics 43713.1 Analyzing Credit Spreads 43813.1.1 Ratings 43813.1.2 Default Probability 44013.1.3 The Severity of Default 44113.2 Modeling Credit Spreads 44113.2.1 Structural Models 44213.2.2 Subsequent Models 44613.2.3 Reduced-Form Models 44813.2.4 Historical versus Risk-Adjusted Probability of Default 45013.3 End of Chapter Summary 45213.4 References and Further Reading 45313.4.1 Books and Papers 45313.4.2 Websites 45413.5 Problems 455Part VII Plain Vanilla Options and More Exotic Derivatives14 Bonds with Embedded Options and Options on Bonds 45914.1 Callable and Putable Bonds 45914.1.1 Institutional Aspects 45914.1.2 Pricing 46014.1.3 OAS Analysis 46714.1.4 Effective Duration and Convexity 46814.2 Convertible Bonds 47014.2.1 Institutional Aspects 47014.2.2 Valuation of Convertible Bonds 47314.2.3 Convertible Arbitrage 47914.3 Options on Bonds 48214.3.1 Definition 48214.3.2 Uses 48314.3.3 Pricing 48714.4 End of Chapter Summary 49114.5 References and Further Reading 49214.5.1 On Callable and Putable Bonds 49214.5.2 On Convertible Bonds 49214.5.3 On Options on Bonds 49314.6 Problems 49414.7 Appendix: Bond Option Prices in the Hull and White (1990) Model 49814.7.1 Call on Zero-Coupon Bond 49914.7.2 Call on Coupon Bond 49915 Options on Futures, Caps, Floors and Swaptions 50015.1 Options on Futures 50015.1.1 Definition and Terminology 50015.1.2 Pricing and Hedging Options on Futures 50215.1.3 Market Quotes 50515.1.4 Uses of Futures Options 50815.2 Caps, Floors and Collars 50815.2.1 Definition and Terminology 50815.2.2 Pricing and Hedging Caps, Floors and Collars 51015.2.3 Market Quotes 51415.2.4 Uses of Caps, Floors and Collars 51615.3 Swaptions 52015.3.1 Definition and Terminology 52015.3.2 Pricing and Hedging Swaptions 52115.3.3 Market Quotes 52615.3.4 Uses of Swaptions 52615.4 End of Chapter Summary 52715.5 References and Further Reading 52815.5.1 Books and Papers 52815.5.2 Websites 52915.6 Problems 52915.7 Appendix 1: Proof of the Cap and Floor Formulas in the Black (1976) Model 53415.8 Appendix 2: Proof of the Swaption Formula in the Black (1976) Model 53515.9 Appendix 3: Forward and Futures Option Prices Written on T-Bond and Libor in the Hull and White (1990) Model 53615.9.1 Options on Forward Contracts 53615.9.2 Options on Futures Contracts 53715.10 Appendix 4: Cap, Floor and Swaption Prices in the Hull and White (1990) Model 53915.10.1 Cap and Floor 53915.10.2 Swaption 54015.11 Appendix 5: Market Models (BGM/Jamshidian Approach) 54115.11.1 Why Define New Variables? 54115.11.2 Building New Variables 54215.11.3 The Dynamics of L(t, θ) and K(t, t + θ) 54315.11.4 Pricing of Caps 54515.11.5 Calibration of the Model 54616 Exotic Options and Credit Derivatives 54816.1 Interest-Rate Exotic Options 54816.1.1 Barrier Caps and Floors 54816.1.2 Bounded Caps, Floors, Barrier Caps and Floors 55016.1.3 Cancelable Swaps 55116.1.4 Captions and Floortions 55116.1.5 Choosercaps and Flexicaps-and-Floors 55116.1.6 Contingent Premium Caps and Floors 55316.1.7 Extendible Swaps 55416.1.8 Incremental Fixed Swaps 55416.1.9 Index Amortizing Bonds and Swaps 55516.1.10 Marked-to-Market Caps 55716.1.11 Moving Average Caps and Floors 55716.1.12 N-Caps and Floors 55816.1.13 Q-Caps and Floors 55816.1.14 Range Accrual Swaps 55916.1.15 Ratchet Caps and Floors 56016.1.16 Reflex Caps and Floors 56116.1.17 Rental Caps and Floors 56216.1.18 Rolling Caps and Floors 56216.1.19 Spread Options 56316.1.20 Subsidized Swaps 56316.1.21 Pricing and Hedging Interest-Rate Exotic Options 56516.2 Credit Derivatives 56516.2.1 The Significance of Credit Derivatives 56516.2.2 Types of Credit Derivatives 56716.3 End of Chapter Summary 57516.4 References and Further Reading 57516.4.1 On Interest-Rate Exotic Options 57516.4.2 On Credit Derivatives 57616.4.3 On Numerical Methods (See the Appendix 2) 57616.4.4 Websites and Others 57716.5 Problems 57716.6 Appendix 1: Pricing and Hedging Barrier Caps and Floors in the Black Model 58016.6.1 Barrier Cap Formulas 58016.6.2 Barrier Floor Formulas 58116.6.3 Barrier Cap and Floor Greeks 58116.7 Appendix 2: Numerical Methods 58316.7.1 Monte Carlo Simulations 58316.7.2 Finite-Difference Methods 585Part VIII Securitization17 Mortgage-Backed Securities 59317.1 Description of MBSs 59317.1.1 Definition 59317.1.2 The Amortization Mechanism 59317.1.3 The Prepayment Feature 59617.1.4 Typology of MBS 59617.2 Market Quotes and Pricing 59817.2.1 Market Quotes 59917.2.2 Pricing of MBS 60017.3 End of Chapter Summary 60317.4 References and Further Reading 60417.4.1 Books and Papers 60417.4.2 Websites 60517.5 Problems 60518 Asset-Backed Securities 60718.1 Description of ABSs 60718.1.1 Definition 60718.1.2 Credit Enhancement 60718.1.3 Cash-Flow Structure 60818.2 Market Quotes and Pricing 61018.3 CAT Bonds and CAT Derivatives 61218.4 End of Chapter Summary 61518.5 References and Further Reading 61518.6 Problems 616Subject Index 617Author Index 629