InterestRate RiskModeling

The Fixed Income Valuation Course

SANJAY K. NAWALKHAGLORIA M. SOTO

NATALIA A. BELIAEVA

John Wiley & Sons, Inc.

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InterestRate RiskModeling

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InterestRate RiskModeling

The Fixed Income Valuation Course

SANJAY K. NAWALKHAGLORIA M. SOTO

NATALIA A. BELIAEVA

John Wiley & Sons, Inc.

Copyright 2005 by Sanjay K. Nawalkha, Gloria M. Soto, and Natalia A. Beliaeva. Allrights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Nawalkha, Sanjay K.Interest rate risk modeling : the fixed income valuation course / Sanjay K.

Nawalkha, Gloria M. Soto, Natalia A. Beliaeva.p. cm.(Wiley finance series)

Includes bibliographical references and index.ISBN-13 978-0-471-42724-7 (cloth / cd-rom)ISBN-10 0-471-42724-1 (cloth / cd-rom)1. Interest rate riskMathematical models. 2. BondsValuationMathematical

models. 3. Fixed-income securitiesValuationMathematical models. I. Title: Fixedincome valuation course. II. Soto, Gloria M. III. Beliaeva, Natalia A. IV. Title. V.Series.

HG6024.5.N39 2005332.6323dc22

2005000048

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

www.wiley.com

To our parentsNatalia and Sanjay

To J. Alberto Gloria

vii

Preface

This is the first book of the trilogy on a fixed-income valuation course by Wiley finance covering the following three areas of fixed-income valuation:

1. Interest rate risk modeling2. Term structure modeling3. Credit risk modeling

Unlike other books in fixed-income valuation, which are either too rig-orous but mathematically demanding, or easy-to-read but lacking in impor-tant details, our goal is to provide readability with sufficient rigor. In thefirst book, we give a basic introduction to various fixed-income securitiesand their derivatives. The principal focus of this book is on measuring andmanaging interest rate risk arising from general nonparallel rate changes inthe term structure of interest rates. This book covers five types of interestrate risk models in the fixed-income literature. These models can be appliedin a variety of contexts by financial institutions ranging from commercialbanks to fixed-income hedge funds. These institutions can design and exe-cute strategies that range from simplest duration-based hedging to the moresophisticated immunization or speculative yield-curve programs, based onmultiple risk measures with off-balance sheet positions in swaps, interestrate options, and interest rate futures.

The five interest rate risk models covered in this book are the durationand convexity models in Chapter 2, M-Absolute/M-Square models in Chap-ter 4, duration vector model in Chapter 5, key rate duration model in Chap-ter 9, and principal component duration model in Chapter 10. Applicationsusing some of these models are given for regular bonds in Chapters 2,4,5,9,and 10; Treasury futures and Eurodollar futures in Chapter 6; bond optionsand callable bonds in Chapter 7; forward rate agreements, interest rate op-tions, swaps, and swaptions in Chapter 8; mortgage securities in Chapter10; and default-prone corporate bonds in Chapter 11.

Chapter 3 also shows how to estimate the term structure of interest ratesfrom a cross-section of bond prices using the Nelson-Siegel exponential

viii PREFACE

model and the McCullochs cubic spline model. The interest rate options,such as caps, floors, collars, and swaptions in Chapter 8 are priced using theLIBOR market models of Jamshidian and others. The default-prone zero-coupon bonds in Chapter 11 are priced using the models of Merton andNawalkha-Shimko et al., while default-prone coupon bonds are priced usingthe first passage probability models of Longstaff and Schwartz, and Collin-Dufresne and Goldstein.

All three books of the trilogy come with software in a user-friendlyexcel/VBA format that covers a variety of models in the three respective areas.The software is organized to correspond with the models covered in differentchapters, so it can be used as a powerful supplement in the learning process.Using the software for the current book, the user could, for example, design amultiple factor hedging strategy using the three key rate durations or usingthe three principal component durations. The user could solve for the no-tional amounts corresponding to interest rate swaps of different maturities toprotect against the height, slope, and curvature shifts in the yield curve usinga three-element duration vector model. The user could pick from a variety ofmultiple factor hedging and speculative strategies, such as immunization,bond index replication, and speculative yield-curve strategies, using a varietyof interest rate contingent claims, such as regular bonds, bond options, Trea-sury futures (on T-bills, T-notes, and T-bonds), Eurodollar futures, forwardrate agreements, interest rate options (e.g., caps, floors, and collars), swaps,swaptions, and default-prone corporate bonds. Finally, based on CraigHoldens excel program, the software for Chapter 3 also demonstrates a ped-agogically useful term structure movie using monthly zero-coupon rates aswell as forward rates over the period from 1946 to 1991.

After reading chapters on given topics from these books, the readershould be able to follow the examples and be ready to apply these modelswithout searching for missing details from other sources (as we often didwhile writing this book). Though many of our programs require codingin advanced scientific languages, such as C, C++, the final output is alwayspresented in user-friendly excel/VBA spreadsheets. These spreadsheets allowthe readers with basic excel skills to instantly play with these models.

This book will be useful to both fixed-income practitioners, as well asgraduate and advanced undergraduate students in an introductory course infixed-income valuation.

Since this book is a part of the trilogy, it is integrated both conceptuallyand in terms of the mathematical notation, with the next two books to fol-low. This implies low cost to the user in reading the next two books, espe-cially for practitioners who do not have the luxury of taking fixed-incomecourses. The second book on term structure modeling covers various termstructure models from the basic Vasicek/CIR models to the more advanced

Preface ix

quadratic, HJM, and LIBOR market models. The third book covers boththe structural and reduced-form models on credit risk as well as valuationof credit derivatives.

Various aspects of this trilogy on the fixed-income valuation course, in-cluding the book descriptions, software details, and future updates areavailable on the web site www.fixedincomerisk.com.

SANJAY K. NAWALKHAGLORIA M. SOTONATALIA A. BELIAEVA

xi

Acknowledgments

We would like to thank the many individuals who helped with this bookproject, some in small ways, others in substantial ways, includingChristopher Schwarz, Aixin Ma, Hossein Kazemi, Bing Liang, NelsonLacey, Sanjiv Das, Huston McCulloch, Hyuna Park, Saira Latif, and YingLi. A special thanks goes to Bill Falloon, the senior editor at John Wiley &Sons, who was supportive, understanding, and patiently gave us extensionson this ever-expanding project.

SANJAY K. NAWALKHAGLORIA M. SOTONATALIA A. BELIAEVA

I would also like to express my gratitude to my wife, Shalini, and my son,Ankrish, who have very patiently loved me through this three-year intenseaffair with my laptop; the Art of Living teachers who showed me how tobeat the stress with the magic of healing breath; and my deeply loving par-ents for their support.

SANJAY K. NAWALKHA

I would like to express my gratitude to Sanjay Nawalkha. His good judg-ment and his ability to bring out the best in everyone involved have un-doubtedly been the driving force behind this book series. I would also liketo thank Philip Thomas for being a real English (he says Welsh) gentlemanand for being there when I needed his particular skills. And finally, I wouldalso like to express my profound gratitude to my parents, Justa and Pablo,

to my brother, Pablo and, in particular, to my husband, J. Alberto, for thesupport and love they have always provided.

GLORIA M. SOTO

I would like to express my gratitude to my family: my husband, Sergei, mydaughter, Sasha, and my parents, Nina and Alexander, for their love andcontinuous support.

NATALIA A. BELIAEVA

xii ACKNOWLEDGMENTS

Contributors

Donald R. Chambers, PhD, serves as the Walter E. Hanson KPMG Chair inFinance at Lafayette College in Easton, Pennsylvania. Dr. Chambers haspublished over 30 articles and frequently serves as a consultant to the alter-native investments industry. Dr. Chambers received his PhD in Finance fromthe University of North Carolina at Chapel Hill.

Cosette Chichirau is the Director of Enterprise Risk Management withMassMutual Financial Group, Springfield, Massachusetts. She is currentlya part-time PhD candidate in finance at the University of Massachusetts,Amherst. She also holds an MBA from the University of Massachusetts,Amherst.

Timothy Crack is a finance professor at Otago University in New Zealand.He is the author of two popular booksHeard on the Street and BasicBlack-Scholes. After graduating from MIT, he first worked as an AssistantProfessor at Indiana University. He then headed a research team at BarclaysGlobal Investors in London. He has also worked as an independent consul-tant to the NYSE.

Iuliana Ismailescu is a PhD candidate in finance at the University of Massa-chusetts, Amherst. She also holds an MBA from Pace University, New York.

Nelson Lacey, CFA, PhD, is an Associate Professor of Finance at the Isen-berg School of Management at the University of Massachusetts, Amherst.Dr. Lacey serves currently as Chairman of the Department of Finance andOperations Management and as the Director of Curriculum and Examina-tions for the Chartered Alternative Investment Analyst Association.

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