Nonparametric Estimation of Jump-Diffusions（531-541）

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1、25NonparametricEstimationofJump-Diffusions*Keywords:kernelmethods,financialeconometrics,estimationofjump-diffusions,simulationWeconsidertheproblemofestimatingdiffusionprocesseswithjumps.Theseprocesseshavebeenwidelyusedfordescribingtherandomevolutionoffinancialfigure

2、ssuchasstockprices,marketindicesandinterestrates.ThiscasedescribesandtestsanonparametricprocedureintroducedinStanton(1997)inacontinuouspathsettingandthenextendedtomixed-jump-diffusionsinJohannes(1999,2004)andBandiandNguyen(1999,2003),whoprovidearigoroustreatmento

3、ftheunderlyingstatisticaltheory.Thetechniqueweillustrateallowsfortheestimationofawidevarietyofhomogeneousdiffusionprocesses,includingthoseforwhichtransitiondensitiesarenotavailableinanalyticform.Weillustratethemethodbydevelopingalgorithmsfortheestimationofbothcon

4、tinuousandmixed-jumpdiffusionprocesses.Weorganizethepresentationasfollows.Section25.1introducesthemainissueofestimatingdiffusionprocessesbyfinitesampledata.Section25.2describesthees-timationtechniquebyspecifyingafinitesampleversionoftheconditionalmomentsfeaturingco

5、ntinuousandmixed-jumpmodels.Section25.3detailsastep-by-stepim-plementationprocedureforallmodelspecifications.Section25.4describesourcodeanddetailsanestimationexperimentbasedonatimeseriesofthe3-monthEURI-BOR,whichisareferenceshort-termrateofinterestintheEuropeanmon

6、eymarket.Resultsaredescribedtogetherwithanassessmentofthequalityoftheproposedpro-cedure.Animportantby-productofouranalysisisthatcontinuousdiffusionmodelsareprovedtobeunabletocaptureimportantfeaturesdisplayedbymarketdata.∗withGiannaFigà-Talamanca.53225Nonparametri

7、cEstimationofJump-Diffusions25.1ProblemStatementWeconsideraone-dimensionaltime-homogeneousdiffusionprocessXdefinedastheuniquesolutionofastochasticdifferentialequationdX(t)=μ(X(t))dt+σ(X(t))dW(t).(25.1)HereWisaone-dimensionalstandardBrownianmotionandμandσareregular

8、functionsensuringexistenceanduniquenessofaweaksolutiontotheequation(25.1)(see,e.g.,KaratzasandShreve(1997)andKloedenandPlaten(2000)).Incidentally,weremarkthatt