Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies pdf

Fixed-Income Securities
Valuation, Risk Management and Portfolio Strategies
Lionel Martellini
Philippe Priaulet
and
St
´
ephane Priaulet

Fixed-Income Securities
Wiley Finance Series
Country Risk Assessment Michael Bouchet, Ephra
¨
ım Clark and Bertrand Groslambert
The Simple Rules of Risk: Revisiting the Art of Risk Management Erik Banks
Measuring Market Risk Kevin Dowd
An Introduction to Market Risk Management Kevin Dowd
Behavioural Finance James Montier
Asset Management: Equities Demystified Shanta Acharya
An Introduction to Capital Markets: Products, Strategies, Participants Andrew M Chisholm
Hedge Funds: Myths and Limits Francois-Serge Lhabitant
The Manager’s Concise Guide to Risk Jihad S Nader
Securities Operations: A guide to trade and position management Michael Simmons
Modeling, Measuring and Hedging Operational Risk Marcelo Cruz
Monte Carlo Methods in Finance Peter J
¨
ackel
Structured Equity Derivatives: The Definitive Guide to Exotic Options and Structured Notes Harry Kat
Advanced Modelling in Finance Using Excel and VBA Mary Jackson and Mike Staunton
Operational Risk: Measurement and Modelling Jack King

Advance Credit Risk Analysis: Financial Approaches and Mathematical Models to Assess, Price and Manage Credit
Risk Didier Cossin and Hugues Pirotte
Interest Rate Modelling Jessica James and Nick Webber
Volatility and Correlation in the Pricing of Equity, FX and Interest-Rate Options Riccardo Rebonato
Risk Management and Analysis vol. 1: Measuring and Modelling Financial Risk Carol Alexander (ed)
Risk Management and Analysis vol. 2: New Markets and Products Carol Alexander (ed)
Interest-Rate Option Models: Understanding, Analysing and Using Models for Exotic Interest-Rate Options (second
edition) Riccardo Rebonato
Fixed-Income Securities
Valuation, Risk Management and Portfolio Strategies
Lionel Martellini
Philippe Priaulet
and
St
´
ephane Priaulet
Copyright
c
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The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should
not in any way be attributed to Philippe Priaulet as a representative, officer or employee of HSBC-CCF.
The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should
not in any way be attributed to St
´
ephane Priaulet as a representative, officer or employee of AXA.
Library of Congress Cataloging-in-Publication Data
Martellini, Lionel.
Fixed-income securities : valuation, risk management, and portfolio strategies / Lionel
Martellini, Philippe Priaulet, and St
´
ephane Priaulet
p. cm. —(Wiley finance series)
Includes bibliographical references and index.
ISBN 0-470-85277-1 (pbk. : alk. paper)
1. Fixed-income securities—Mathematical models. 2. Portfolio
management—Mathematical models. 3. Bonds—Mathematical models. 4. Hedging
(Finance)—Mathematical models. I. Priaulet, Philippe. II. Priaulet, St
´

ephane. III. Title. IV.
Series.
HG4650.M367 2003
332.63

2044—dc21 2003041167
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0-470-85277-1
Typeset in 10/12.5pt Times by Laserwords Private Limited, Chennai, India
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire
This book is printed on acid-free paper responsibly manufactured from sustainable forestry
in which at least two trees are planted for each one used for paper production.
To Adhara, Antonella, Calypso, Daphn´e, Isabelle and Manon
To our parents and families
To our friends

Contents
About the Authors xix
Preface xxi
Acknowledgments xxv
Notation xxvii
PART I
INVESTMENT ENVIRONMENT
1 Bonds and Money-Market Instruments 3
1.1 Bonds
3
1.1.1 General Characteristics of Bonds 3
1.1.2 Bonds by Issuers 17
1.2 Money-Market Instruments 25

1.2.1 Definition 25
1.2.2 The Role of the Central Bank 25
1.2.3 T-Bills 26
1.2.4 Certificates of Deposit 28
1.2.5 Bankers’ Acceptances 29
1.2.6 Commercial Papers 29
1.2.7 Interbank Deposits 30
1.2.8 Repo and Reverse Repo Market Instruments 30
1.3 End of Chapter Summary 32
1.4 References and Further Reading 33
1.4.1 Books and Papers 33
1.4.2 Websites and Others 33
1.5 Problems 34
1.5.1 Problems on Bonds 34
1.5.2 Problems on Money-Market Instruments 36
1.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan
Corporate Bond Markets
37
2 Bond Prices and Yields 41
2.1 Introduction to Bond Pricing
41
2.2 Present Value Formula 43
viii
Contents
2.2.1 Time-Value of Money 43
2.2.2 The Mathematics of Discounting 43
2.2.3 Nominal versus Real Interest Rates 45
2.2.4 Time Basis and Compounding
Frequency Conventions
46

2.2.5 Continuous Compounding 47
2.3 Taxonomy of Rates 49
2.3.1 Coupon Rate and Current Yield 49
2.3.2 Yield to Maturity 49
2.3.3 Spot Zero-Coupon (or Discount) Rate 51
2.3.4 Forward Rates 52
2.3.5 Bond Par Yield 54
2.4 End of Chapter Summary 54
2.5 References and Further Reading 54
2.6 Problems 55
PART II
TERM STRUCTURE OF INTEREST RATES
3 Empirical Properties and Classical Theories of the Term Structure 63
3.1 Definition and Properties of the Term Structure
63
3.1.1 What Kind of Shape Can It Take? 65
3.1.2 How Does It Evolve over Time? 68
3.2 Classical Theories of the Term Structure 81
3.2.1 The Pure Expectations Theory 82
3.2.2 The Pure Risk Premium Theory 83
3.2.3 The Market Segmentation Theory 85
3.2.4 The Biased Expectations Theory:
An Integrated Approach
86
3.2.5 Illustration and Empirical Validation 86
3.2.6 Summary and Extensions 87
3.3 End of Chapter Summary 88
3.4 References and Further Reading 89
3.4.1 On the Empirical Behavior of the Yield Curve 89
3.4.2 On the Principal Component Analysis

of the Yield Curve
90
3.4.3 On the Classical Theories of the Term Structure
of Interest Rates
90
3.5 Problems 91
4 Deriving the Zero-Coupon Yield Curve 96
4.1 Deriving the Nondefault Treasury Zero-Coupon Yield Curve
96
4.1.1 How to Select a Basket of Bonds? 96
4.1.2 Direct Methods 97
4.1.3 Indirect Methods 103
ix
Contents
4.2 Deriving the Interbank Zero-Coupon Rate Curve 130
4.2.1 How to Select the Basket of Instruments? 130
4.2.2 Interpolation Methods 132
4.2.3 Least Squares Methods Based on Rates 132
4.2.4 Least Squares Methods Based on Prices 133
4.3 Deriving Credit Spread Term Structures 136
4.3.1 Disjoint Methods 136
4.3.2 Joint Methods 137
4.4 End of Chapter Summary 142
4.5 References and Further Reading 144
4.6 Problems 146
4.7 Appendix: A Useful Modified Newton’s Algorithm 155
PART III
HEDGING INTEREST-RATE RISK
5 Hedging Interest-Rate Risk with Duration 163
5.1 Basics of Interest-Rate Risk: Qualitative Insights

163
5.1.1 The Five Theorems of Bond Pricing 163
5.1.2 Reinvestment Risk 164
5.1.3 Capital Gain Risk 165
5.1.4 Qualifying Interest-Rate Risk 166
5.2 Hedging with Duration 167
5.2.1 Using a One-Order Taylor Expansion 167
5.2.2 Duration, $Duration and Modified Duration 170
5.2.3 How to Hedge in Practice? 173
5.3 End of Chapter Summary 175
5.4 References and Further Reading 176
5.4.1 Books 176
5.4.2 Papers 176
5.5 Problems 177
6 Beyond Duration 182
6.1 Relaxing the Assumption of a Small Shift
182
6.1.1 Using a Second-Order Taylor Expansion 182
6.1.2 Properties of Convexity 185
6.1.3 Hedging Method 187
6.2 Relaxing the Assumption of a Parallel Shift 188
6.2.1 A Common Principle 188
6.2.2 Regrouping Risk Factors through
a Principal Component Analysis
192
6.2.3 Hedging Using a Three-Factor Model
of the Yield Curve
195
6.3 End of Chapter Summary 199
x

Contents
6.4 References and Further Reading 200
6.5 Problems 201
PART IV
INVESTMENT STRATEGIES
7 Passive Fixed-Income Portfolio Management 213
7.1 Straightforward Replication
213
7.2 Replication by Stratified Sampling 214
7.3 Tracking-Error Minimization 216
7.3.1 Optimization Procedure 216
7.3.2 Bond Return Covariance Matrix Estimation 217
7.4 Factor-Based Replication 226
7.5 Derivatives-Based Replication 229
7.6 Pros and Cons of Stratified Sampling versus
Tracking-Error Minimization
230
7.7 End of Chapter Summary 230
7.8 References and Further Reading 231
7.8.1 Books and Papers 231
7.8.2 Websites 231
7.9 Problems 231
8 Active Fixed-Income Portfolio Management 233
8.1 Market Timing: Trading on Interest-Rate Predictions
233
8.1.1 Timing Bets on No Change in the Yield Curve
or “Riding the Yield Curve”
234
8.1.2 Timing Bets on Interest-Rate Level 236
8.1.3 Timing Bets on Specific Changes in the

Yield Curve
238
8.1.4 Scenario Analysis 251
8.1.5 Active Fixed-Income Style Allocation Decisions 255
8.2 Trading on Market Inefficiencies 268
8.2.1 Trading within a Given Market: The Bond
Relative Value Analysis
269
8.2.2 Trading across Markets: Spread
and Convergence Trades
276
8.3 End of Chapter Summary 282
8.4 References and Further Reading 283
8.4.1 On Active Fixed-Income Strategies 283
8.4.2 On Active Asset Allocation Decisions 284
8.4.3 Others 286
8.5 Problems 286
9 Performance Measurement on Fixed-Income Portfolios 293
9.1 Return Measures
293
9.1.1 Arithmetic Rate of Return 293
9.1.2 Geometric Rate of Return 294
xi
Contents
9.2 Risk-Adjusted Performance Evaluation 295
9.2.1 Absolute Risk-Adjusted Performance Evaluation 296
9.2.2 Relative Risk-Adjusted Performance Evaluation 299
9.3 Application of Style Analysis to Performance Evaluation
of Bond Portfolio Managers: An Example
309

9.3.1 Alpha Analysis 310
9.3.2 Passive Versus Active Managers 313
9.4 End of Chapter Summary 314
9.5 References and Further Reading 315
9.5.1 Books and Papers 315
9.5.2 Websites 316
9.6 Problems 316
PART V
SWAPS AND FUTURES
10 Swaps 325
10.1 Description of Swaps
325
10.1.1 Definition 325
10.1.2 Terminology and Conventions 325
10.2 Pricing and Market Quotes 326
10.2.1 Pricing of Swaps 326
10.2.2 Market Quotes 333
10.3 Uses of Swaps 334
10.3.1 Optimizing the Financial Conditions of a Debt 335
10.3.2 Converting the Financial Conditions of a Debt 336
10.3.3 Creating New Assets Using Swaps 337
10.3.4 Hedging Interest-Rate Risk Using Swaps 339
10.4 Nonplain Vanilla Swaps 342
10.4.1 Accrediting, Amortizing and Roller Coaster Swaps 342
10.4.2 Basis Swap 343
10.4.3 Constant Maturity Swap and Constant
Maturity Treasury Swap
343
10.4.4 Forward-Starting Swap 344
10.4.5 Inflation-Linked Swap 344

10.4.6 Libor in Arrears Swap 344
10.4.7 Yield-Curve Swap 345
10.4.8 Zero-Coupon Swap 345
10.5 End of Chapter Summary 346
10.6 References and Further Reading 346
10.6.1 Books and Papers 346
10.6.2 Websites 347
10.7 Problems 347
xii
Contents
11 Forwards and Futures 353
11.1 Definition
353
11.2 Terminology, Conventions and Market Quotes 354
11.2.1 Terminology and Conventions 354
11.2.2 Quotes 356
11.3 Margin Requirements and the Role of the Clearing House 358
11.4 Conversion Factor and the Cheapest-to-Deliver Bond 359
11.4.1 The Cheapest to Deliver on the Repartition Date 360
11.4.2 The Cheapest to Deliver before
the Repartition Date
361
11.5 Pricing of Forwards and Futures 362
11.5.1 Forward-Spot Parity or How to Price
a Forward Contract?
362
11.5.2 The Forward Contract Payoff 364
11.5.3 Relation between Forward and Futures Prices 365
11.6 Uses of Forwards and Futures 365
11.6.1 Pure Speculation with Leverage Effect 365

11.6.2 Fixing Today the Financial Conditions of a Loan
or Investment in the Future
366
11.6.3 Detecting Riskless Arbitrage Opportunities
Using Futures
367
11.6.4 Hedging Interest-Rate Risk Using Futures 368
11.7 End of Chapter Summary 370
11.8 References and Further Reading 371
11.8.1 Books and Papers 371
11.8.2 Websites of Futures Markets and of the Futures
Industry Association
371
11.9 Problems 372
11.10 Appendix: Forward and Futures Prices Are Identical
When Interest Rates Are Constant
375
PART VI
MODELING THE TERM STRUCTURE OF INTEREST RATES AND CREDIT SPREADS
12 Modeling the Yield Curve Dynamics 381
12.1 The Binomial Interest-Rate Tree Methodology
382
12.1.1 Building an Interest-Rate Tree 382
12.1.2 Calibrating an Interest-Rate Tree 384
12.2 Continuous-Time Models 387
12.2.1 Single-Factor Models 388
12.2.2 Multifactor Models 392
12.3 Arbitrage Models 396
xiii
Contents

12.3.1 A Discrete-Time Example: Ho and Lee’s
Binomial Lattice
396
12.3.2 Arbitrage Models in Continuous Time 401
12.4 End of Chapter Summary 406
12.5 References and Further Reading 407
12.6 Problems 411
12.7 Appendix 1: The Hull and White Trinomial Lattice 413
12.7.1 Discretizing the Short Rate 413
12.7.2 Calibrating the Lattice to the Current
Spot Yield Curve
416
12.7.3 Option Pricing 419
12.8 Appendix 2: An Introduction to Stochastic
Processes in Continuous Time
420
12.8.1 Brownian Motion 420
12.8.2 Stochastic Integral 423
12.8.3 Stochastic Differential Equations (SDE) 425
12.8.4 Asset Price Process 426
12.8.5 Representation of Brownian Martingales 426
12.8.6 Continuous-Time Asset Pricing 427
12.8.7 Feynman–Kac Formula 431
12.8.8 Application to Equilibrium Models
of the Term Structure
432
13 Modeling the Credit Spreads Dynamics 437
13.1 Analyzing Credit Spreads
438
13.1.1 Ratings 438

13.1.2 Default Probability 440
13.1.3 The Severity of Default 441
13.2 Modeling Credit Spreads 441
13.2.1 Structural Models 442
13.2.2 Subsequent Models 446
13.2.3 Reduced-Form Models 448
13.2.4 Historical versus Risk-Adjusted
Probability of Default
450
13.3 End of Chapter Summary 452
13.4 References and Further Reading 453
13.4.1 Books and Papers 453
13.4.2 Websites 454
13.5 Problems 455
PART VII
PLAIN VANILLA OPTIONS AND MORE EXOTIC DERIVATIVES
14 Bonds with Embedded Options and Options on Bonds 459
14.1 Callable and Putable Bonds
459
xiv
Contents
14.1.1 Institutional Aspects 459
14.1.2 Pricing 460
14.1.3 OAS Analysis 467
14.1.4 Effective Duration and Convexity 468
14.2 Convertible Bonds 470
14.2.1 Institutional Aspects 470
14.2.2 Valuation of Convertible Bonds 473
14.2.3 Convertible Arbitrage 479
14.3 Options on Bonds 482

14.3.1 Definition 482
14.3.2 Uses 483
14.3.3 Pricing 487
14.4 End of Chapter Summary 491
14.5 References and Further Reading 492
14.5.1 On Callable and Putable Bonds 492
14.5.2 On Convertible Bonds 492
14.5.3 On Options on Bonds 493
14.6 Problems 494
14.7 Appendix: Bond Option Prices in the Hull
and White (1990) Model
498
14.7.1 Call on Zero-Coupon Bond 499
14.7.2 Call on Coupon Bond 499
15 Options on Futures, Caps, Floors and Swaptions 500
15.1 Options on Futures
500
15.1.1 Definition and Terminology 500
15.1.2 Pricing and Hedging Options on Futures 502
15.1.3 Market Quotes 505
15.1.4 Uses of Futures Options 508
15.2 Caps, Floors and Collars 508
15.2.1 Definition and Terminology 508
15.2.2 Pricing and Hedging Caps, Floors and Collars 510
15.2.3 Market Quotes 514
15.2.4 Uses of Caps, Floors and Collars 516
15.3 Swaptions 520
15.3.1 Definition and Terminology 520
15.3.2 Pricing and Hedging Swaptions 521
15.3.3 Market Quotes 526

15.3.4 Uses of Swaptions 526
15.4 End of Chapter Summary 527
15.5 References and Further Reading 528
15.5.1 Books and Papers 528
15.5.2 Websites 529
15.6 Problems 529
xv
Contents
15.7 Appendix 1: Proof of the Cap and Floor
Formulas in the Black (1976) Model
534
15.8 Appendix 2: Proof of the Swaption Formula
in the Black (1976) Model
535
15.9 Appendix 3: Forward and Futures Option Prices Written on T-Bond
and Libor in the Hull and White (1990) Model
536
15.9.1 Options on Forward Contracts 536
15.9.2 Options on Futures Contracts 537
15.10 Appendix 4: Cap, Floor and Swaption Prices in the Hull
and White (1990) Model
539
15.10.1 Cap and Floor 539
15.10.2 Swaption 540
15.11 Appendix 5: Market Models (BGM/Jamshidian Approach) 541
15.11.1 Why Define New Variables? 541
15.11.2 Building New Variables 542
15.11.3 The Dynamics of L(t, θ) and K(t,t + θ) 543
15.11.4 Pricing of Caps 545
15.11.5 Calibration of the Model 546

16 Exotic Options and Credit Derivatives 548
16.1 Interest-Rate Exotic Options
548
16.1.1 Barrier Caps and Floors 548
16.1.2 Bounded Caps, Floors, Barrier Caps and Floors 550
16.1.3 Cancelable Swaps 551
16.1.4 Captions and Floortions 551
16.1.5 Choosercaps and Flexicaps-and-Floors 551
16.1.6 Contingent Premium Caps and Floors 553
16.1.7 Extendible Swaps 554
16.1.8 Incremental Fixed Swaps 554
16.1.9 Index Amortizing Bonds and Swaps 555
16.1.10 Marked-to-Market Caps 557
16.1.11 Moving Average Caps and Floors 557
16.1.12 N-Caps and Floors 558
16.1.13 Q-Caps and Floors 558
16.1.14 Range Accrual Swaps 559
16.1.15 Ratchet Caps and Floors 560
16.1.16 Reflex Caps and Floors 561
16.1.17 Rental Caps and Floors 562
16.1.18 Rolling Caps and Floors 562
16.1.19 Spread Options 563
16.1.20 Subsidized Swaps 563
16.1.21 Pricing and Hedging Interest-Rate Exotic Options 565
xvi
Contents
16.2 Credit Derivatives 565
16.2.1 The Significance of Credit Derivatives 565
16.2.2 Types of Credit Derivatives 567
16.3 End of Chapter Summary 575

16.4 References and Further Reading 575
16.4.1 On Interest-Rate Exotic Options 575
16.4.2 On Credit Derivatives 576
16.4.3 On Numerical Methods (See the Appendix 2) 576
16.4.4 Websites and Others 577
16.5 Problems 577
16.6 Appendix 1: Pricing and Hedging Barrier Caps and Floors
in the Black Model
580
16.6.1 Barrier Cap Formulas 580
16.6.2 Barrier Floor Formulas 581
16.6.3 Barrier Cap and Floor Greeks 581
16.7 Appendix 2: Numerical Methods 583
16.7.1 Monte Carlo Simulations 583
16.7.2 Finite-Difference Methods 585
PART VIII
SECURITIZATION
17 Mortgage-Backed Securities 593
17.1 Description of MBSs
593
17.1.1 Definition 593
17.1.2 The Amortization Mechanism 593
17.1.3 The Prepayment Feature 596
17.1.4 Typology of MBS 596
17.2 Market Quotes and Pricing 598
17.2.1 Market Quotes 599
17.2.2 Pricing of MBS 600
17.3 End of Chapter Summary 603
17.4 References and Further Reading 604
17.4.1 Books and Papers 604

17.4.2 Websites 605
17.5 Problems 605
18 Asset-Backed Securities 607
18.1 Description of ABSs
607
18.1.1 Definition 607
18.1.2 Credit Enhancement 607
18.1.3 Cash-Flow Structure 608
xvii
Contents
18.2 Market Quotes and Pricing 610
18.3 CAT Bonds and CAT Derivatives 612
18.4 End of Chapter Summary 615
18.5 References and Further Reading 615
18.6 Problems 616
Subject Index 617
Author Index 629

About the Authors
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 Trading and Management and The Journal of Alternative
Investments. He holds master’s degrees in business administration, economics,
statistics and mathematics, as well as a Ph.D. in finance from the Haas School of
Business, University of California at Berkeley. His expertise is in derivatives valuation and optimal
portfolio strategies, and his research has been published in leading academic and practitioners’
journals. He has also served as a consultant for various international institutions on these subjects.
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. He holds master’s degrees
in business administration and mathematics as well as a Ph.D. in financial eco-
nomics from University Paris IX Dauphine. Member of the editorial board of The
Journal of Bond Trading and Management, he is also an associate professor in the
Department of Mathematics of the University of Evry Val d’Essonne and a lecturer at ENSAE,
where he teaches “fixed-income securities” and “interest rate modeling”.
St
´
ephane Priaulet is senior index portfolio manager in the Structured Asset Man-
agement Department at AXA Investment Managers. Previously, he was head
of quantitative 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 sev-
eral research papers. He holds a diploma from the HEC School of Management,
with specialization in economics and finance, and has completed postgraduate
studies in mathematics at the University Pierre et Marie Curie (Paris VI), with
specialization in stochastic calculus.

Preface
Debt instruments have evolved beyond the straight bonds with simple cash-flow structures to
securities with increasingly complex cash-flow structures that attract a wider range of investors
and enable borrowers to reduce their costs of raising funds. In order to effectively employ portfolio
strategies that may control interest-rate risk and/or enhance returns, investors must understand the
forces that drive bond markets and the valuation of these complex securities and their derivative
products.
What this Book is About

This book is about interest rates and risk management in bond markets. It develops insights into
different bond portfolio strategies and illustrates how various types of derivative securities can
be used to shift the risks associated with investing in fixed-income securities. It also provides
extensive coverage on all sectors of the bond market and the techniques for valuing bonds.
While there certainly exists an impressive list of books that cover in some detail the issues related
to bond and fixed-income derivative pricing and hedging, we just could not find, in existing
textbooks, the same level of depth in the analysis of active and passive bond portfolio strategies.
This is perhaps unfortunate because we have learnt a lot about active and passive bond portfolio
strategies in the past thirty years or so. While no financial economist or practitioner in the industry
would claim they have found a reliable model for the valuation of stocks, we indeed have reached
a fairly high level of understanding on how, why and when to invest in bonds.
We have written this book in an attempt to achieve the following goal: provide the reader with
a detailed exposure to modern state-of-the-art techniques for bond portfolio management. We
cover not only traditional techniques used by mutual fund managers in the fixed-income area but
also advanced techniques used by traders and hedge fund managers engaged in fixed-income or
convertible arbitrage strategies.
More specifically, we attempt to achieve the following:
• Describe important financial instruments that have market values that are sensitive to interest-
rate movements. Specifically, the course will survey the following fixed-income assets and
related securities: zero-coupon government bonds, coupon-bearing government bonds, cor-
porate bonds, exchange-traded bond options, bonds with embedded options, floating-rate
notes, caps, collars and floors, floating-rate notes with embedded options, forward contracts,
interest-rate swaps, bond futures and options on bond futures, swaptions, credit derivatives,
mortgage-backed securities, and so on.
• Develop tools to analyze interest-rate sensitivity and value fixed-income securities. Specifi-
cally, the course will survey the following tools for active and passive bond management:
xxii
Preface
construction of discount functions, duration, convexity, and immunization; binomial trees for
analysis of options; hedging with bond futures, using models of the term structure for pricing

and hedging fixed-income securities; models for performance evaluation; systematic approach
to timing; valuation of defaultable bonds; bonds with embedded options; interest-rate deriva-
tives, and so on.
For the Reader
This book is original in that it aims at mixing theoretical and practical aspects of the question in
a systematic way. This duality can be traced back to the professional orientations of the authors,
who are active in both the academic and the industrial worlds. As such, this book can be of interest
to both students and professionals from the banking industry. To reach the goal of providing the
reader with a practical real-world approach to the subject, we have ensured that the book contains
detailed presentations of each type of bond and includes a wide range of products. Extensive
discussions include not only the instruments but also their investment characteristics, the state-of-
the art technology for valuing them and portfolio strategies for using them. We make a systematic
use of numerical examples to facilitate the understanding of these concepts.
The level of mathematical sophistication required for a good understanding of most of the material
is relatively limited and essentially includes basic notions of calculus and statistics. When more
sophisticated mathematical tools are needed, they are introduced in a progressive way and most
really advanced material has been placed in dedicated appendices. As a result, the book is suited
to students and professionals with various exposure to, or appetite for, a more quantitative treat-
ment of financial concepts. Generally speaking, the material devoted to the modeling of the term
structure and the pricing of interest-rate derivatives is more technical, even though we have con-
sistently favored intuition and economic analysis over mathematical developments. Appendix 2 to
Chapter 12, devoted to advanced mathematical tools for term-structure modeling, can be skipped by
the nonquantitatively oriented reader without impeding his/her ability to understand the remaining
six chapters.
For the Instructor
The book is complemented with a set of problems (more than 200 of them) and their solutions,
posted on a dedicated website (www.wiley.co.uk/martellini), as well as a complete set of Excel
illustrations and PowerPoint slides (more than 400 of them). This makes it ideally suited for
a typical MBA audience, in the context of a basic or more advanced “Fixed-Income Security”
course. It can also be used by undergraduate, graduate and doctoral students in finance.

The first nine chapters offer a detailed analysis of all issues related to bond markets, including
institutional details, methods for constructing the yield curve and hedging interest-rate risk, as well
as a detailed overview of active and passive bond portfolio strategies and performance evaluation.
As such, they form a coherent whole that can be used for a shorter quarter course on the subject.
Chapters 10 to 18 cover a whole range of fixed-income securities, including swaps, futures, options,
and so on. This second half of the book provides a self-contained study of the modern approach
for pricing and hedging fixed-income securities and interest-rate options. The text mostly focuses
on the binomial approach to the pricing of fixed-income derivatives, providing cutting-edge theory