[Andrew Davidson & Co] Interest Rate Modeling - A Conscientious Choice

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1、..ERSPECTIVESPINTERESTRATEMODELING:ACONSCIENTIOUSCHOICEUANTITATIVEByALEXLEVINQSeptember2002INTERESTRATEMODELING:ACONSCIENTIOUSCHOICEByAlexLevinSEPTEMBER2002QUANTITATIVEPERSPECTIVES..IntroductionIntensivedevelopmentsinthefieldofinterestratemodelinghavedeliveredaboldbutconfusingmodels

2、electionchoiceforfinancialengineers,riskmanagers,andinvestmentanalysts.Dothesemodelingissuessoundfamiliar?!ShouldamortgagebankassesstheinterestrateriskusingthelognormalBlack-KarasinskimodelorusingthenormalHull-Whitemodel?!Canaportfoliobehedgedusingdifferentpricingmodelsforassetsandd

3、erivatives?!Isthereanyhistoricalevidencethatonemodelisbetterthananother?!Whatdoesthemarket"think"abouttheinterestratedistribution?(Itmust"know"something-otherwisehowwouldtherateoptionsbetraded?)InthisissueofQuantitativePerspectives,weshowthatselectingthe"best"termstructuremodelisbec

4、omingmoreofaconscientioustaskthanamatteroftaste.Weshowthatbothrecenthistoricalratesandimpliedvolatilityskewforswaptionsconfirmrate"normalization"andrejecttheconjectureoflognormality.WeproposevaluingmortgagesusingtheHull-Whitemodel,whichcanbequicklyandaccuratelycalibratedtoboththeyie

5、ldcurveandtheswaptionvolatilitymatrix.Beingfullyawareofthesemarketindicationsandtendencies,wehaveexpandedandenhancedourVectorsTMsuiteofanalyticalmodels.Lognormality:TheOldDaysThosewhoreadresearchonhowinterestratesperformedin1980sandearly1990sareaccustomedtotheconjectureoflognormalit

6、y.Accordingtoit,interestratesarelognormallydistributed,i.e.,theirlogarithmisnormallydistributed.Therates,therefore,cannotbecomenegative,andtheirrandomnessshouldbenaturallyandsteadilymeasuredbyrelativevolatility.ThisconjecturehadenforcedthevalidityandapplicabilityoftheBlack-Scholespr

7、icingmodeltotheinterestrateoptionmarket.FollowingPaulWilmott[1998]wewillbemeasuringvolatilitybyplottingtheaverageddailyincrementsversustheratelevel.Namely,wecancollectalldailyrateincrementsandstoretheminbuckets;eachbucketcorrespondstosomeratelevel.Forexample,a7%bucketincludesalldail

8、yincrementswhenther