The Generalized Hyperbolic Model Estimation,

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1、TheGeneralizedHyperbolicModel:Estimation,FinancialDerivatives,andRiskMeasuresDissertationzurErlangungdesDoktorgradesderMathematischenFakult¨atderAlbert-Ludwigs-Universit¨atFreiburgi.Br.vorgelegtvonKarstenPrauseOktober1999Dekan:Prof.Dr.WolfgangSoergelReferenten:Prof.Dr.ErnstEberl

2、einProf.Ph.D.BentJesperChristensenDatumderPromotion:15.Dezember1999Institutf¨urMathematischeStochastikAlbert-Ludwigs-Universit¨atFreiburgEckerstrae1D{79104FreiburgimBreisgauToUlrikePrefaceTheaimofthisdissertationistodescribemorerealisticmodelsfornancialassetsbasedongeneralized

3、hyperbolic(GH)distributionsandtheirsubclasses.GeneralizedhyperbolicdistributionswereintroducedbyBarndor-Nielsen(1977),andstochasticprocessesbasedonthesedistributionswererstappliedbyEberleinandKeller(1995)inFinance.Beinganormalvariance-meanmixture,GHdistributionspossesssemi-hea

4、vytailsandallowforanaturaldenitonofvolatilitymodelsbyreplacingthemixinggeneralizedinverseGaussian(GIG)distributionbyappropriatevolatilityprocesses.IntherstChapterweintroduceunivariateGHdistributions,constructanestimationalgorithmandexaminestatisticallythetofgeneralizedhyperbo

5、licdistributionstolog-returndistributionsofnancialassets.WeextendthehyperbolicmodelforthepricingofderivativestogeneralizedhyperbolicLevymotionsanddiscussthecalculationofpricesbyfastFouriermethodsandsaddle-pointapproximations.Chapter2containsontheonehandageneralrecipefortheeval

6、uationofoptionpricingmodels;ontheotherhandthederivativepricingbasedonGHLevymotionsisstudiedfromvariouspointsofview:Theaccordancewithobservedassetpriceprocessesisinvestigatedstatistically,andbysimulationstudiesthesensitivitytorelevantvariables;nally,theoreticalpricesarecompared

7、withquotedoptionprices.Furthermore,weexaminetwoapproachestomartingalemodellinganddiscussalternativewaystotestoptionpricingmodels.Barndor-Nielsen(1998)proposedarenementoftheGHLevymodelbyreplacingthemixingGIGdistributionbyavolatilityprocessoftheOrnstein-Uhlenbecktype.Weinvesti-

8、gatethismodelinChapter3withaviewtowardsderivati