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Dynamic Term Structure Modeling The Fixed Income Valuation Course SANJAY K. NAWALKHA NATALIA A. BELIAEVA GLORIA M. SOTO John Wiley & Sons, Inc. Dynamic Term Structure Modeling Founded in 1807, John Wiley & Sons is the oldest independent publishing companyintheUnitedStates.WithofficesinNorthAmerica,Europe,Aus- tralia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional andpersonalknowledgeandunderstanding. TheWileyFinanceseriescontainsbookswrittenspecificallyforfinance and investment professionals as well as sophisticated individual investors andtheirfinancialadvisors.Booktopicsrangefromportfoliomanagement to e-commerce, risk management, financial engineering, valuation, and financialinstrumentanalysis,aswellasmuchmore. Foralistofavailabletitles,visitourWebsiteatwww.WileyFinance.com. Dynamic Term Structure Modeling The Fixed Income Valuation Course SANJAY K. NAWALKHA NATALIA A. BELIAEVA GLORIA M. SOTO John Wiley & Sons, Inc. Copyright(cid:1)c 2007bySanjayK.Nawalkha,NataliaA.Beliaeva,andGloriaM.Soto.All rightsreserved. PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey. PublishedsimultaneouslyinCanada. WileyBicentennialLogo:RichardJ.Pacifico. Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin anyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,or otherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyright Act,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthrough paymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222 RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)646-8600,orontheWeb atwww.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothe PermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030, (201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions. 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Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,please contactourCustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outside theUnitedStatesat(317)572-3993orfax(317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsin printmaynotbeavailableinelectronicbooks.FormoreinformationaboutWileyproducts, visitourWebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Nawalkha,SanjayK. Dynamictermstructuremodeling:thefixedincomevaluationcourse/ SanjayK.Nawalkha,NataliaA.Beliaeva,GloriaM.Soto. p.cm.—(Wileyfinanceseries) Includesbibliographicalreferencesandindex. ISBN978-0-471-73714-8(cloth/cd-rom) 1. Finance. 2. Stochasticprocesses. I. Beliaeva,N.A.(Natal’ia Anatol’evna) II. Soto,GloriaM. III. Title. HG101.N392007 332.01(cid:2)51923—dc22 2006037555 PrintedintheUnitedStatesofAmerica. 10 9 8 7 6 5 4 3 2 1 To Sri Sri Ravi Shankar —SanjayK.Nawalkha To my family —NataliaA.Beliaeva To my parents —GloriaM.Soto Preface T hisisthesecondbookofthetrilogyonafixedincomevaluation course by Wiley finance. This trilogy covers the following three areas of fixed incomevaluation: 1. Interestrateriskmodeling 2. Termstructuremodeling 3. Creditriskmodeling Unlike other books in fixed income valuation, which are either too rigorous but mathematically demanding or easy-to-read but lacking in important details, our goal is to provide readability with sufficient rigor. In the first book, we gave a basic introduction to various fixed income securitiesandtheirderivatives.Theprincipalfocusofthefirstbookwason measuringandmanaging interestrateriskarisingfromgeneralnonparallel ratechangesinthetermstructureofinterestrates.Duetosmoothnessinthe shapesoftermstructures,interestrateriskofstraightbondscanbemanaged even without a proper valuation model simply by using empiricalduration vectorsorempiricalkeyratedurationprofiles.Infact,asdemonstratedinthe firstbook,InterestRateRiskModeling,basicinterestrateriskmanagement of financial institutions such as commercial banks, fixed income funds, insurance companies, and pension funds can be done without using the mostsophisticatedvaluationmodels. In this second book, we shift our focus to valuation of fixed income securities and their derivatives. A good valuation model is a key input not onlyforsupportingthefixedincometradingdesksoffinancialinstitutions, but also for designing comprehensive risk management strategies for these institutions. The basic tools of fixed income valuation are ‘‘dynamic term structure models,’’ which are also loosely referred to as ‘‘interest rate models.’’ This second book in the trilogy aims to bridge the gap between the advanced technical books in the term structure area and the many elementarydiscussionsoftermstructuremodelsinthegeneralfixedincome tradebooks.Bychoosingbasicmathematicalruleswithheuristicderivations over rigorous theoretical developments with technical proofs, we hope to make this difficult subject matter accessible to the wider audience of financial analysts, students, and academics. The readers will also benefit vii