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ID:40372278
大小:2.02 MB
页数:168页
时间:2019-08-01
《The Generalized Hyperbolic Model Estimation, 》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
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{79104FreiburgimBreisgauToUlrikePrefaceTheaimofthisdissertationistodescribemorerealisticmodelsfornancialassetsbasedongeneralized
3、hyperbolic(GH)distributionsandtheirsubclasses.GeneralizedhyperbolicdistributionswereintroducedbyBarndor-Nielsen(1977),andstochasticprocessesbasedonthesedistributionswererstappliedbyEberleinandKeller(1995)inFinance.Beinganormalvariance-meanmixture,GHdistributionspossesssemi-hea
4、vytailsandallowforanaturaldenitonofvolatilitymodelsbyreplacingthemixinggeneralizedinverseGaussian(GIG)distributionbyappropriatevolatilityprocesses.IntherstChapterweintroduceunivariateGHdistributions,constructanestimationalgorithmandexaminestatisticallythetofgeneralizedhyperbo
5、licdistributionstolog-returndistributionsofnancialassets.WeextendthehyperbolicmodelforthepricingofderivativestogeneralizedhyperbolicLevymotionsanddiscussthecalculationofpricesbyfastFouriermethodsandsaddle-pointapproximations.Chapter2containsontheonehandageneralrecipefortheeval
6、uationofoptionpricingmodels;ontheotherhandthederivativepricingbasedonGHLevymotionsisstudiedfromvariouspointsofview:Theaccordancewithobservedassetpriceprocessesisinvestigatedstatistically,andbysimulationstudiesthesensitivitytorelevantvariables;nally,theoreticalpricesarecompared
7、withquotedoptionprices.Furthermore,weexaminetwoapproachestomartingalemodellinganddiscussalternativewaystotestoptionpricingmodels.Barndor-Nielsen(1998)proposedarenementoftheGHLevymodelbyreplacingthemixingGIGdistributionbyavolatilityprocessoftheOrnstein-Uhlenbecktype.Weinvesti-
8、gatethismodelinChapter3withaviewtowardsderivati
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