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Fixed Income Securities: Tools for Today's Markets, 2nd Edition

ISBN: 978-0-471-35615-8
528 pages
October 2002
Fixed Income Securities: Tools for Today


Praise for Fixed Income Securities, Second Edition

"What distinguishes this book from many others on the subject is that Tuckman has skillfully combined intuitive rationale with mathematical analysis to give readers a clear and deep understanding of the market. Tuckman has written a comprehensive reference book that should be found on the desks of both seasoned practitioners and novices alike." Gerald Lucas, Senior Government Strategist, Director, Global Securities Research, Merrill Lynch

"This outstanding book offers a well-written and clear tutorial for many of the cutting-edge analytical techniques and models used in practice. Combines a wealth of institutional knowledge, practical tools, and realistic examples, while giving a clear understanding of the underlying theory." Francis Longstaff, Professor of Finance, The Anderson School at UCLA

"An excellent reference for anyone intending to bridge the gap between financial mathematics theory and the practice of financial markets." Marek Musiela, BNP Paribas

"This is an extremely readable book with a balance between technical detail and practical application. Unlike other books in the area, thorough and tightly knit chapters reflect Tuckman s unique background as a well-respected academic and market participant." Tony D. Kao, Managing Director, Global Fixed Income GM Asset Management
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Table of Contents



PART ONE: The Relative Pricing of Fixed Income Securities with Fixed Cash Flows.

CHAPTER 1: Bond Prices, Discount Factors, and Arbitrage.

The Time Value of Money.

Treasury Bond Quotations.

Discount Factors.

The Law of One Price.

Arbitrage and the Law of One Price. Treasury STRIPS.

APPENDIX 1A: Deriving the Replicating Portfolio.

APPENDIX 1B: APPLICATION: Treasury Triplets and High Coupon Bonds.

CHAPTER 2: Bond Prices, Spot Rates, and Forward Rates.

Semiannual Compounding.

Spot Rates.

Forward Rates.

Maturity and Bond Price.

Maturity and Bond Return.

Treasury STRIPS, Continued.

APPENDIX 2A: The Relation between Spot and Forward Rates and the Slope of the Term Structure.

CHAPTER 3: Yield-to-Maturity.

Definition and Interpretation.

Yield-to-Maturity and Spot Rates.

Yield-to-Maturity and Relative Value: The Coupon Effect.

Yield-to-Maturity and Realized Return.

CHAPTER 4: Generalizations and Curve Fitting.

Accrued Interest.

Compounding Conventions.

Yield and Compounding Conventions.

Bad Days.

Introduction to Curve Fitting.

Piecewise Cubics.

APPLICATION: Fitting the Term Structure in the U.S. Treasury Market on February 15, 2001.

TRADING CASE STUDY: A 7s-8s-9s Butterfly.

APPENDIX 4A: Continuous Compounding.

APPENDIX 4B: A Simple Cubic Spline.

PART TWO: Measures of Price Sensitivity and Hedging.

CHAPTER 5: One-Factor Measures of Price Sensitivity.


A Hedging Example, Part I: Hedging a Call Option.



A Hedging Example, Part II: A Short Convexity Position.

Estimating Price Changes and Returns with DV01, Duration, and Convexity.

Convexity in the Investment and Asset-Liability Management Contexts.

Measuring the Price Sensitivity of Portfolios.

A Hedging Example, Part III: The Negative Convexity of Callable Bonds.

CHAPTER 6: Measures of Price Sensitivity Based on Parallel Yield Shifts.

Yield-Based DV01.

Modified and Macaulay Duration.

Zero Coupon Bonds and a Reinterpretation of Duration.

Par Bonds and Perpetuities.

Duration, DV01, Maturity, and Coupon: A Graphical Analysis.

Duration, DV01, and Yield.

Yield-Based Convexity.

Yield-Based Convexity of Zero Coupon Bonds.

The Barbell versus the Bullet.

CHAPTER 7: Key Rate and Bucket Exposures.

Key Rate Shifts.

Key Rate 01s and Key Rate Durations.

Hedging with Key Rate Exposures.

Choosing Key Rates.

Bucket Shifts and Exposures.


Multi-Factor Exposures and Risk Management.

CHAPTER 8: Regression-Based Hedging.

Volatility-Weighted Hedging.

One-Variable Regression-Based Hedging.

Two-Variable Regression-Based Hedging.

TRADING CASE STUDY: The Pricing of the 20-Year U.S. Treasury Sector.

A Comment on Level Regressions.

PART THREE: Term Structure Models.

CHAPTER 9: The Science of Term Structure Models.

Rate and Price Trees.

Arbitrage Pricing of Derivatives.

Risk-Neutral Pricing.

Arbitrage Pricing in a Multi-Period Setting.

Example: Pricing a CMT Swap.

Reducing the Time Step.

Fixed Income versus Equity Derivatives.

CHAPTER 10: The Short-Rate Process and the Shape of the Term Structure.


Volatility and Convexity.

Risk Premium.

A Mathematical Description of Expectations, Convexity, and Risk Premium.

APPLICATION: Expectations, Convexity, and Risk Premium in the U.S. Treasury Market on February 15, 2001.

APPENDIX 10A: Proofs of Equations (10.19) and (10.25).

CHAPTER 11: The Art of Term Structure Models: Drift.

Normally Distributed Rates, Zero Drift: Model 1.

Drift and Risk Premium: Model 2.

Time-Dependent Drift: The Ho-Lee Model.

Desirability of Fitting to the Term Structure.

Mean Reversion: The Vasicek (1977) Model.

CHAPTER 12: The Art of Term Structure Models: Volatility and Distribution.

Time-Dependent Volatility: Model 3.

Volatility as a Function of the Short Rate: The Cox-Ingersoll-Ross and Lognormal Models.

Tree for the Original Salomon Brothers Model.

A Lognormal Model with Mean Reversion: The Black-Karasinski Model.

Selected List of One-Factor Term Structure Models.

APPENDIX 12A: Closed-Form Solutions for Spot Rates.

CHAPTER 13: Multi-Factor Term Structure Models.

Motivation from Principal Components.

A Two-Factor Model.

Tree Implementation.

Properties of the Two-Factor Model.

Other Two-Factor and Multi-Factor Modeling Approaches.

APPENDIX 13A: Closed-Form Solution for Spot Rates in the Two-Factor Model.

CHAPTER 14: Trading with Term Structure Models.

Example Revisited: Pricing a CMT Swap.

Option-Adjusted Spread.

Profit and Loss (P&L) Attribution.

P&L Attributions for a Position in the CMT Swap.

TRADING CASE STUDY: Trading 2s-5s-10s in Swaps with a Two-Factor Model.

Fitting Model Parameters.

Hedging to the Model versus Hedging to the Market.

PART FOUR: Selected Securities.

CHAPTER 15: Repo.

Repurchase Agreements and Cash Management.

Repurchase Agreements and Financing Long Positions.

Reverse Repurchase Agreements and Short Positions.


General Collateral and Specials.

Special Repo Rates and the Auction Cycle.

Liquidity Premiums of Recent Issues.

APPLICATION: Valuing a Bond Trading Special in Repo.

APPLICATION: Disruption in the Specials Market after September 11, 2001.

CHAPTER 16: Forward Contracts.


Forward Price of a Deposit or a Zero Coupon Bond.

Using Forwards to Hedge Borrowing Costs or Loan Proceeds.

Forward Price of a Coupon Bond.

Forward Yield and Forward DV01.

Forward Prices with Intermediate Coupon Payments.

Value of a Forward Contract.

Forward Prices in a Term Structure Model.

CHAPTER 17: Eurodollar and Fed Funds Futures.

LIBOR and Eurodollar Futures.

Hedging with Eurodollar Futures.

Tails: A Closer Look at Hedging with Futures.

Futures on Prices in a Term Structure Model.

Futures on Rates in a Term Structure Model.

The Futures-Forward Difference.

TED Spreads.

APPLICATION: Trading TED Spreads.

Fed Funds.

Fed Funds Futures.

APPLICATION: Fed Funds Contracts and Predicted Fed Action.

APPENDIX 17A: Hedging to Dates Not Matching Fed Funds and Eurodollar Futures Expirations.

CHAPTER 18: Interest Rate Swaps.

Swap Cash Flows.

Valuation of Swaps.

Floating Rate Notes.

Valuation of Swaps, Continued.

Note on the Measurement of Fixed and Floating Interest Rate Risk.

Swap Spreads.

Major Uses of Interest Rate Swaps.

Asset Swap Spreads and Asset Swaps.

TRADING CASE STUDY: 30-Year FNMA Asset Swap Spreads.

On the Credit Risk of Swap Agreements.

APPENDIX 18A: TRADING CASE STUDY: Five-Year On-the-Run/Off-the-Run Spread of Spreads.

CHAPTER 19: Fixed Income Options.

Definitions and Review.

Pricing American and Bermudan Bond Options in a Term Structure Model.

APPLICATION: FNMA 6.25s of July 19, 2011, and the Pricing of Callable Bonds.

Graphical Analysis of Callable Bond Pricing.

A Note on Yield-to-Call.

Swaptions, Caps, and Floors.

Quoting Prices with Volatility Measures in Fixed Income Options Markets.

Smile and Skew.

CHAPTER 20: Note and Bond Futures.


Cost of Delivery and the Determination of the Final Settlement Price.

Motivations for a Delivery Basket and Conversion Factors.

Imperfection of Conversion Factors and the Delivery Option at Expiration.

Gross and Net Basis.

Quality Option before Delivery.

Some Notes on Pricing the Quality Option in Term Structure Models.

Measures of Rate Sensitivity.

Timing Option.

End-of-Month Option.

TRADING CASE STUDY: November '08 Basis into TYM0.

CHAPTER 21: Mortgage-Backed Securities.

Basic Mortgage Mathematics.

Prepayment Option.

Overview of Mortgage Pricing Models.

Implementing Prepayment Models.

Price-Rate Curve of a Mortgage Pass-Through.

APPLICATION: Mortgage Hedging and the Directionality of Swap Spreads.

Mortgage Derivatives, IOs, and Pos.




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Author Information

BRUCE TUCKMAN, PhD, is a Managing Director in the Fixed Income and Derivatives Division of Credit Suisse First Boston. After receiving his doctorate in economics from MIT, he became a professor of finance at New York University's Stern School of Business and a visiting professor at UCLA's Anderson Graduate School of Management. He began his Wall Street career at Salomon Brothers' Fixed Income Proprietary Trading Group.
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"Required reading for anyone interested in modeling fixed income securities. In my opinion, this edition of Tuckman's book has no match in terms of clarity, accessibility and applicability to today's bond markets." ( Vineer Bhansali, Ph.D. Executive Vice President Head of Portfolio Analytics PIMCO)
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