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1、EstimatingthevolatilitytermstructureAntonioD´ıaz,FranciscoJareno,andEliseoNavarro˜Abstract.Inthispaper,weproceedtoestimatetermstructureofinterestratevolatilities,findingthattheseestimatesdependsignificantlyonthemodelusedtoestimatethetermstructure(NelsonandSiegelorVasicekandF
2、ong)andtheheteroscedasticitystructureoferrors(OLSorGLSweightedbyduration).Weconcludeinourempiricalanalysisthattherearesignificantdifferencesbetweenthesevolatilitiesintheshort(lessthanoneyear)andlongterm(morethantenyears).Finally,wecandetectthatthreeprincipalcomponentsexplai
3、n90%ofthechangesinvolatilitytermstructure.Thesecomponentsarerelatedtolevel,slopeandcurvature.Keywords:volatilitytermstructure(VTS),termstructureofinterestrates(TSIR),GARCH,principalcomponents(PCs)1IntroductionWedefinethetermstructureofvolatilitiesastherelationshipbetweenthe
4、volatil-ityofinterestratesandtheirmaturities.Theimportanceofthisconcepthasbeengrowingoverrecentdecades,particularlyasinterestratederivativeshavedevelopedandinterestratevolatilityhasbecomethekeyfactorforthevaluationofassetssuchascaplets,caps,floors,swaptions,etc.Moreover,int
5、erestratevolatilityisoneoftheinputsneededtoimplementsometermstructuremodelssuchasthoseofBlack,DermanandToy[4]orHullandWhite[12],whichareparticularlypopularamongpractitioners.However,oneofthemainproblemsconcerningtheestimationofthevolatilitytermstructure(VTS)arisesfromthefa
6、ctthatzerocouponratesareunobservable.Sotheymustbepreviouslyestimatedandthisrequirestheadoptionofaparticularmethodology.Theproblemofthetermstructureestimationisanoldquestionwidelyanalysedintheliteratureandseveralprocedureshavebeensuggestedoverthelastthirtyyears.Amongthemost
7、popularmethodsarethosedevelopedbyNelsonandSiegel[14]andVasicekandFong[17].InSpain,thesemethodshavebeenappliedinNu´nez[15]˜andContrerasetal.[7]respectively.Alargebodyofliteraturefocusesonthebondvaluationabilityofthesealternativemodelswithoutanalysingtheimpactofthetermstruct
8、ureestimationmethodonM.Corazzaetal.(eds.),MathematicalandStatisticalMethodsforActuarialSc
